Engineering Functions¶

This contains the list of engineering functions that are currently supported by Codcel.

B¶

BESSELI ¶

Calculates the modified Bessel function of the first kind.

Purpose: This function is used in engineering and mathematical computations to solve problems involving modified Bessel differential equations of the first kind.
Formula: BESSELI(x, n)
- x is the value at which to evaluate the Bessel function.
- n is the order of the Bessel function.
Example Usage:
- =BESSELI(3.5, 2) calculates the modified Bessel function of the first kind for x = 3.5 and order n = 2.
- =BESSELI(A1, A2) computes the modified Bessel function using cell references, where A1 is the value for x and A2 is the order n.

BESSELJ ¶

Calculates the Bessel function of the first kind.

Purpose: This function is used in engineering and mathematical computations to solve problems involving Bessel differential equations of the first kind.
Formula: BESSELJ(x, n)
x is the value at which to evaluate the Bessel function.
n is the order of the Bessel function.
Example Usage:
=BESSELJ(3.5, 2) calculates the Bessel function of the first kind for x = 3.5 and order n = 2.
=BESSELJ(A1, A2) computes the Bessel function using cell references, where A1 is the value for x and A2 is the order n.

BESSELK ¶

Calculates the modified Bessel function of the second kind.

Purpose: This function is used in engineering and mathematical computations to solve problems involving modified Bessel differential equations of the second kind.
Formula: BESSELK(x, n)
x is the value at which to evaluate the Bessel function.
n is the order of the Bessel function.
Example Usage:
=BESSELK(3.5, 2) calculates the modified Bessel function of the second kind for x = 3.5 and order n = 2.
=BESSELK(A1, A2) computes the modified Bessel function using cell references, where A1 is the value for x and A2 is the order n.

BESSELY ¶

Calculates the Bessel function of the second kind.

Purpose: This function is used in engineering and mathematical computations to solve problems involving Bessel differential equations of the second kind.
Formula: BESSELY(x, n)
x is the value at which to evaluate the Bessel function.
n is the order of the Bessel function.
Example Usage:
=BESSELY(3.5, 2) calculates the Bessel function of the second kind for x = 3.5 and order n = 2.
=BESSELY(A1, A2) computes the Bessel function using cell references, where A1 is the value for x and A2 is the order n.

BIN2DEC ¶

Converts a binary number to its decimal equivalent.

Purpose: This function is used to convert a binary (base-2) number into its decimal (base-10) equivalent, which is commonly used in engineering, mathematics, and computing.
Formula: BIN2DEC(text)
text is the binary string that you want to convert to a decimal number. The binary string can have up to 10 characters (0s and 1s) and may represent either positive or negative numbers using two's complement representation.
Example Usage:
=BIN2DEC("1101") converts the binary number 1101 into the decimal value 13.
=BIN2DEC("1111111111") converts the binary number 1111111111 into the decimal value -1 (two's complement).

BIN2HEX ¶

Converts a binary number to its hexadecimal equivalent.

Purpose: This function is used to convert a binary (base-2) number into its hexadecimal (base-16) equivalent, commonly used in computing and engineering.
Formula: BIN2HEX(text, [places])
text is the binary string that you want to convert to a hexadecimal number. The binary string can have up to 10 characters (0s and 1s).
places (optional): Specifies the number of characters in the hexadecimal result. If the result has fewer characters than the value specified, leading zeroes are added. If omitted, Excel uses the minimum number of characters necessary.
Example Usage:
=BIN2HEX("1101") converts the binary number 1101 into the hexadecimal value D.
=BIN2HEX("1111111101") converts the binary number 1111111101 into the hexadecimal value 3FD (two's complement for negative numbers).

BIN2OCT ¶

Converts a binary number to its octal equivalent.

Purpose: This function is used to convert a binary (base-2) number into its octal (base-8) equivalent, commonly used in computing and engineering.
Formula: BIN2OCT(text, [places])
text is the binary string that you want to convert to an octal number. The binary string can have up to 10 characters (0s and 1s).
places (optional): Specifies the number of characters in the octal result. If the result has fewer characters than the value specified, leading zeroes are added. If omitted, Excel uses the minimum number of characters necessary.
Example Usage:
=BIN2OCT("1101") converts the binary number 1101 into the octal value 15.
=BIN2OCT("1111111101") converts the binary number 1111111101 into the octal value 7775 (two's complement for negative numbers).

BITAND ¶

Performs a bitwise AND operation on two numbers.

Purpose: This function is used to perform a bitwise AND operation, often used in engineering, computing, and digital logic design.
Formula: BITAND(number1, number2)
number1 is the first non-negative integer.
number2 is the second non-negative integer.
Example Usage:
=BITAND(5, 3) computes the bitwise AND of the numbers 5 (101 in binary) and 3 (011 in binary), resulting in 1 (001 in binary).
=BITAND(A1, A2) computes the bitwise AND operation using cell references, where A1 and A2 are non-negative integers.

BITLSHIFT ¶

Performs a bitwise left shift operation on a number.

Purpose: This function is used to perform a bitwise left shift operation, often applied in engineering, computing, and digital logic.
Formula: BITLSHIFT(number, shift_amount)
number is the non-negative integer to be shifted.
shift_amount is the number of positions to shift the bits to the left. Non-negative integer values are expected. If the shift_amount is 0, the function returns the original number.
Example Usage:
=BITLSHIFT(5, 2) computes a bitwise left shift of the number 5 (101 in binary), shifting it 2 positions to the left, resulting in 20 (10100 in binary).
=BITLSHIFT(A1, A2) computes the bitwise left shift operation using cell references, where A1 is the number to shift, and A2 is the shift amount.

BITOR ¶

Performs a bitwise OR operation on two numbers.

Purpose: This function is used to perform a bitwise OR operation, often used in engineering, computing, and digital logic design.
Formula: BITOR(number1, number2)
number1 is the first non-negative integer.
number2 is the second non-negative integer.
Example Usage:
=BITOR(5, 3) computes the bitwise OR of the numbers 5 (101 in binary) and 3 (011 in binary), resulting in 7 (111 in binary).
=BITOR(A1, A2) computes the bitwise OR operation using cell references, where A1 and A2 are non-negative integers.

BITRSHIFT ¶

Performs a bitwise right shift operation on a number.

Purpose: This function is used to perform a bitwise right shift operation, often applied in engineering, computing, and digital logic.
Formula: BITRSHIFT(number, shift_amount)
number is the non-negative integer to be shifted.
shift_amount is the number of positions to shift the bits to the right. Non-negative integer values are expected. If the shift_amount is 0, the function returns the original number.
Example Usage:
=BITRSHIFT(20, 2) computes a bitwise right shift of the number 20 (10100 in binary), shifting it 2 positions to the right, resulting in 5 (101 in binary).
=BITRSHIFT(A1, A2) computes the bitwise right shift operation using cell references, where A1 is the number to shift, and A2 is the shift amount.

BITXOR ¶

Performs a bitwise XOR operation on two numbers.

Purpose: This function is used to perform a bitwise XOR operation, often used in engineering, computing, and digital logic design.
Formula: BITXOR(number1, number2)
number1 is the first non-negative integer.
number2 is the second non-negative integer.
Example Usage:
=BITXOR(5, 3) computes the bitwise XOR of the numbers 5 (101 in binary) and 3 (011 in binary), resulting in 6 (110 in binary).
=BITXOR(A1, A2) computes the bitwise XOR operation using cell references, where A1 and A2 are non-negative integers.

DEC2BIN ¶

Converts a decimal number to its binary equivalent.

Purpose: This function is used to convert a decimal (base-10) number into its binary (base-2) equivalent, commonly used in computing and digital logic.
Formula: DEC2BIN(number, [places])
number is the decimal integer you want to convert to binary. It can be a positive or negative value.
places (optional): Specifies the number of characters in the binary result.
If the result has fewer characters than the value specified, leading zeroes are added.
If omitted, the function uses the minimum number of characters necessary.
Example Usage:
=DEC2BIN(13) converts the decimal number 13 into the binary value 1101.
=DEC2BIN(-1) converts the decimal number -1 into the binary value 1111111111 (two's complement representation with a width of 10 bits).
=DEC2BIN(13, 8) converts the decimal number 13 into the binary value 00001101, ensuring the result has 8 characters.

DEC2HEX ¶

Converts a decimal number to its hexadecimal equivalent.

Purpose: This function is used to convert a decimal (base-10) number into its hexadecimal (base-16) equivalent, commonly used in computing and engineering.
Formula: DEC2HEX(number, [places])
number is the decimal integer you want to convert to hexadecimal. It can be a positive or negative value.
places (optional): Specifies the number of characters in the hexadecimal result.
If the result has fewer characters than the value specified, leading zeroes are added.
If omitted, the function uses the minimum number of characters necessary.
Example Usage:
=DEC2HEX(255) converts the decimal number 255 into the hexadecimal value FF.
=DEC2HEX(-1) converts the decimal number -1 into the hexadecimal value FFFFFFFF (two's complement representation with a width of 32 bits by default).
=DEC2HEX(255, 4) converts the decimal number 255 into the hexadecimal value 00FF, ensuring the result has 4 characters.

DEC2OCT ¶

Converts a decimal number to its octal equivalent.

Purpose: This function is used to convert a decimal (base-10) number into its octal (base-8) equivalent, commonly used in computing and engineering.
Formula: DEC2OCT(number, [places])
number is the decimal integer you want to convert to octal. It can be a positive or negative value.
places (optional): Specifies the number of characters in the octal result.
If the result has fewer characters than the value specified, leading zeroes are added.
If omitted, the function uses the minimum number of characters necessary.
Example Usage:
=DEC2OCT(10) converts the decimal number 10 into the octal value 12.
=DEC2OCT(-1) converts the decimal number -1 into the octal value 7777777777 (two's complement representation with a width of 10 bits).
=DEC2OCT(8, 4) converts the decimal number 8 into the octal value 0010, ensuring the result has 4 characters.

DELTA ¶

Checks whether two numbers are equal, returning 1 if they are equal and 0 otherwise.

Purpose: This function is used to compare two numbers and check if they are equal, commonly used in engineering, computing, and mathematical calculations.
Formula: DELTA(number1, number2)
number1 is the first number to compare.
number2 is the second number to compare. If omitted, the default value is 0.
Behavior:
Returns 1 if number1 equals number2.
Returns 0 otherwise.
Example Usage:
=DELTA(5, 5) returns 1 because the numbers are equal.
=DELTA(5, 3) returns 0 because the numbers are not equal.
=DELTA(5) returns 0 because 5 is not equal to the default value of 0.

ERF ¶

Calculates the error function (ERF) of a number.

Purpose: This function is used to compute the error function, which is commonly used in probability, statistics, and partial differential equations.
Formula: ERF(lower_limit, [upper_limit])
lower_limit is the lower bound of the integral for calculating the error function.
upper_limit (optional) is the upper bound of the integral.
If omitted, the error function is calculated from 0 to lower_limit.
Behavior:
If both lower_limit and upper_limit are provided, the function calculates the integral of the Gaussian probability density function between the two bounds.
If upper_limit is omitted, the function defaults to calculating ERF from 0 to lower_limit.
Example Usage:
=ERF(1) calculates the error function from 0 to 1, resulting in approximately 0.8427.
=ERF(1, 2) calculates the error function from 1 to 2, resulting in approximately 0.1359.
=ERF(-1) calculates the error function from 0 to -1, resulting in approximately -0.8427.

ERFPRECISE ¶

Calculates the precise error function (ERF) of a number with a higher degree of accuracy.

Purpose: This function is used to compute the error function with higher precision, commonly used in probability, statistics, and mathematical calculations requiring greater accuracy.
Formula: ERF.PRECISE(number)
number is the point at which the error function needs to be evaluated.
Example Usage:
=ERF.PRECISE(1) calculates the error function at 1, resulting in approximately 0.8427 with higher precision.
=ERF.PRECISE(-1) calculates the error function at -1, resulting in approximately -0.8427 with higher precision.
=ERF.PRECISE(2) calculates the error function at 2, resulting in approximately 0.9953 with higher precision.

ERFC ¶

Calculates the complementary error function (ERFC) of a number.

Purpose: This function is used to compute the complementary error function, which is commonly used in probability, statistics, and mathematical calculations.
Formula: ERFC(number)
number is the point at which the complementary error function needs to be evaluated.
Behavior:
The complementary error function is defined as 1 - ERF(number).
Example Usage:
=ERFC(1) calculates the complementary error function at 1, resulting in approximately 0.1573.
=ERFC(-1) calculates the complementary error function at -1, resulting in approximately 1.8427.
=ERFC(2) calculates the complementary error function at 2, resulting in approximately 0.0047.

ERFC.PRECISE ¶

Calculates the complementary error function (ERFC) of a number with a higher degree of accuracy.

Purpose: This function is used to compute the complementary error function with higher precision, commonly used in probability, statistics, and mathematical calculations requiring greater accuracy.
Formula: ERFC.PRECISE(number)
number is the point at which the complementary error function needs to be evaluated.
Example Usage:
=ERFC.PRECISE(1) calculates the complementary error function at 1, resulting in approximately 0.1573 with higher precision.
=ERFC.PRECISE(-1) calculates the complementary error function at -1, resulting in approximately 1.8427 with higher precision.
=ERFC.PRECISE(2) calculates the complementary error function at 2, resulting in approximately 0.0047 with higher precision.

G¶

GESTEP ¶

Returns 1 if a number is greater than or equal to a step value, and 0 otherwise.

Purpose: This function is used to test whether a number is greater than or equal to a specified step value. It is commonly used in logical comparisons and engineering calculations.
Formula: GESTEP(number, [step])
number is the value to test.
step (optional) is the threshold value for comparison. If omitted, the default value is 0.
Behavior:
Returns 1 if number is greater than or equal to step.
Returns 0 otherwise.
Example Usage:
=GESTEP(5, 3) returns 1 because 5 is greater than or equal to 3.
=GESTEP(2, 5) returns 0 because 2 is not greater than or equal to 5.
=GESTEP(0) returns 1 because 0 is greater than or equal to the default step value of 0.

H¶

HEX2BIN ¶

Converts a hexadecimal number to its binary equivalent.

Purpose: This function is used to convert a hexadecimal (base-16) number into its binary (base-2) equivalent, commonly used in computing and engineering.
Formula: HEX2BIN(number, [places])
number is the hexadecimal value you want to convert to binary. It can be a positive or negative value.
places (optional): Specifies the number of characters in the binary result.
If the result has fewer characters than the value specified, leading zeroes are added.
If omitted, the function uses the minimum number of characters necessary.
Example Usage:
=HEX2BIN("F") converts the hexadecimal value F into the binary value 1111.
=HEX2BIN("F", 8) converts the hexadecimal value F into the binary value 00001111, ensuring the result has 8 characters.
=HEX2BIN("2A", 16) converts the hexadecimal value 2A into the binary value 0000000000101010, ensuring the result has 16 characters.

HEX2DEC ¶

Converts a hexadecimal number to its decimal equivalent.

Purpose: This function is used to convert a hexadecimal (base-16) number into its decimal (base-10) equivalent, commonly used in computing and engineering.
Formula: HEX2DEC(number)
number is the hexadecimal value you want to convert to decimal. It can be a positive or negative value.
Example Usage:
=HEX2DEC("F") converts the hexadecimal value F into the decimal value 15.
=HEX2DEC("2A") converts the hexadecimal value 2A into the decimal value 42.
=HEX2DEC("-1F") converts the hexadecimal value -1F into the decimal value -31.

HEX2OCT ¶

Converts a hexadecimal number to its octal equivalent.

Purpose: This function is used to convert a hexadecimal (base-16) number into its octal (base-8) equivalent, commonly used in computing and engineering.
Formula: HEX2OCT(number, [places])
number is the hexadecimal value you want to convert to octal. It can be a positive or negative value.
places (optional): Specifies the number of characters in the octal result.
If the result has fewer characters than the value specified, leading zeroes are added.
If omitted, the function uses the minimum number of characters necessary.
Example Usage:
=HEX2OCT("F") converts the hexadecimal value F into the octal value 17.
=HEX2OCT("F", 4) converts the hexadecimal value F into the octal value 0017, ensuring the result has 4 characters.
=HEX2OCT("2A", 6) converts the hexadecimal value 2A into the octal value 000052, ensuring the result has 6 characters.

IMABS ¶

Calculates the absolute value (modulus) of a complex number.

Purpose: This function is used to return the absolute value (or modulus) of a complex number, helpful in complex number arithmetic.
Formula: IMABS(inumber)
inumber is the complex number for which you want the absolute value. It can be in the form x+yi or x+yj.
Example Usage:
=IMABS("3+4i") returns 5, since the modulus of 3 + 4i is √(3² + 4²) = 5.
=IMABS("-3-4i") returns 5 because the modulus depends only on the magnitude, not the sign.
=IMABS("0+2i") returns 2, as it's the distance of 2i from 0.

IMARGUMENT ¶

Calculates the argument (angle in radians) of a complex number.

Purpose: This function is used to calculate the angle (in radians) formed by a complex number in the complex plane with respect to the positive real axis. It is commonly used in engineering, physics, and mathematics when working with complex numbers.
Formula: IMARGUMENT(inumber)
inumber is the complex number for which you want to calculate the argument. It can be in the form x+yi or x+yj.
Example Usage:
=IMARGUMENT("1+i") returns approximately 0.7854, which is π/4, as it forms a 45-degree angle.
=IMARGUMENT("-1-i") returns approximately -2.3562, which is -3π/4.
=IMARGUMENT("0+1i") returns 1.5708, which is π/2 as it lies on the positive imaginary axis.
=IMARGUMENT("3") returns 0, as it lies on the positive real axis.

IMCONJUGATE ¶

Calculates the complex conjugate of a complex number.

Purpose: This function is used to return the complex conjugate of a complex number, where the sign of the imaginary part is reversed. Useful in various applications involving complex number arithmetic.
Formula: IMCONJUGATE(inumber)
inumber is the complex number for which you want the conjugate. It can be in the form x+yi or x+yj.
Example Usage:
=IMCONJUGATE("3+4i") returns 3-4i, as the conjugate of 3+4i is 3-4i.
=IMCONJUGATE("-2-5j") returns -2+5j, reversing the sign of the imaginary part.
=IMCONJUGATE("0+2i") returns -2i, where only the imaginary part changes.
=IMCONJUGATE("5") returns 5, as real numbers are unchanged when conjugated.

IMCOS ¶

Calculates the cosine of a complex number.

Purpose: This function is used to return the cosine of a complex number, helpful in engineering and mathematical calculations involving trigonometric functions of complex numbers.
Formula: IMCOS(inumber)
inumber is the complex number for which you want to calculate the cosine. It can be in the form x+yi or x+yj.
Example Usage:
=IMCOS("0") returns 1, as the cosine of 0 is 1.
=IMCOS("i") returns approximately 1.5431, as the cosine of i is cosh(1).
=IMCOS("1+i") returns approximately 0.83373 - 0.9889i, as the cosine is calculated using both the real and imaginary components.
=IMCOS("-1-2i") returns approximately -1.5656 - 3.2979i.

IMCOSH ¶

Calculates the hyperbolic cosine of a complex number.

Purpose: This function is used to return the hyperbolic cosine of a complex number, which is helpful in engineering and mathematical calculations involving hyperbolic functions of complex numbers.
Formula: IMCOSH(inumber)
inumber is the complex number for which you want to calculate the hyperbolic cosine. It can be in the form x+yi or x+yj.
Example Usage:
=IMCOSH("0") returns 1, as the hyperbolic cosine of 0 is 1.
=IMCOSH("i") returns approximately 0.5403 + 0.0i, as the hyperbolic cosine of i is cos(1).
=IMCOSH("1+i") returns approximately 0.83373 + 0.9889i, as the hyperbolic cosine is calculated using both the real and imaginary components.
=IMCOSH("-1-2i") returns approximately -0.6421 - 1.0688i.

IMCOT ¶

Calculates the cotangent of a complex number.

Purpose: This function is used to return the cotangent of a complex number, helpful in engineering and mathematical calculations involving trigonometric functions of complex numbers.
Formula: IMCOT(inumber)
inumber is the complex number for which you want to calculate the cotangent. It can be in the form x+yi or x+yj.
Example Usage:
=IMCOT("1") returns approximately 0.6421 - 0.0i, as cotangent is the reciprocal of tangent.
=IMCOT("i") returns approximately 0.0 - 0.7616i.
=IMCOT("1+i") returns approximately 0.2176 - 0.8680i, as cotangent is calculated using both the real and imaginary components.
=IMCOT("-1-2i") returns approximately -0.0338 + 0.0753i.

IMCSC ¶

Calculates the cosecant of a complex number.

Purpose: This function is used to return the cosecant (reciprocal of sine) of a complex number, helpful in engineering and mathematical calculations involving trigonometric functions of complex numbers.
Formula: IMCSC(inumber)
inumber is the complex number for which you want to calculate the cosecant. It can be in the form x+yi or x+yj.
Example Usage:
=IMCSC("1") returns approximately 1.1884 + 0.0i, as cosecant is the reciprocal of sine.
=IMCSC("i") returns approximately 0.0 - 0.8509i.
=IMCSC("1+i") returns approximately 0.6215 - 0.3039i, as the cosecant is calculated using the reciprocal of sine for both the real and imaginary components.
=IMCSC("-1-2i") returns approximately -0.2284 - 0.1414i.

IMCSCH ¶

Calculates the hyperbolic cosecant of a complex number.

Purpose: This function is used to return the hyperbolic cosecant (reciprocal of hyperbolic sine) of a complex number, helpful in engineering and mathematical calculations involving hyperbolic functions of complex numbers.
Formula: IMCSCH(inumber)
inumber is the complex number for which you want to calculate the hyperbolic cosecant. It can be in the form x+yi or x+yj.
Example Usage:
=IMCSCH("1") returns approximately 0.8509 - 0.0i, as hyperbolic cosecant is the reciprocal of hyperbolic sine.
=IMCSCH("i") returns approximately 0.0 - 1.1884i.
=IMCSCH("1+i") returns approximately 0.3039 - 0.6215i, calculated as the reciprocal of the hyperbolic sine of both real and imaginary components.
=IMCSCH("-1-2i") returns approximately -0.1414 - 0.2284i.

IMDIV ¶

Calculates the quotient of two complex numbers.

Purpose: This function is used to divide one complex number by another, useful in various engineering, physics, and mathematics applications involving complex number arithmetic.
Formula: IMDIV(inumber1, inumber2)
inumber1 is the complex number you want to divide (numerator). It can be in the form x+yi or x+yj.
inumber2 is the complex number you want to divide by (denominator). It can be in the form x+yi or x+yj.

The formula for dividing complex numbers is:

(a + bi) / (c + di) = [(a*c + b*d) + (b*c - a*d)i] / (c² + d²)

Example Usage:
=IMDIV("3+4i", "1+i") returns 3.5 + 0.5i, dividing 3+4i by 1+i.
=IMDIV("1", "2+i") returns approximately 0.4 - 0.2i.
=IMDIV("0+2i", "3+4i") returns approximately 0.32 + 0.24i, dividing purely imaginary numbers.
=IMDIV("4", "0+i") returns 0 - 4i, dividing a real number by an imaginary number.
=IMDIV("2+i", "0") returns an error, as division by zero is undefined.

IMEXP ¶

Calculates the exponential of a complex number.

Purpose: This function is used to compute the exponential of a complex number, which is often required in engineering, physics, and mathematics for dealing with growth processes or oscillatory phenomena.
Formula: IMEXP(inumber)
inumber is the complex number for which you want to calculate the exponential. It can be in the form x+yi or x+yj.
The formula for the exponential of a complex number is:
```
e^(a + bi) = e^a * [cos(b) + i*sin(b)]
```
Example Usage:
=IMEXP("0") returns 1, as e^0 = 1.
=IMEXP("1") returns approximately 2.7183, as e^1 = 2.7183.
=IMEXP("i") returns approximately 0.5403 + 0.8415i, as e^(i) = cos(1) + i*sin(1).
=IMEXP("1+i") returns approximately 1.4687 + 2.2874i, using the formula to calculate both real and imaginary components.
=IMEXP("-1-2i") returns approximately -0.0677 - 0.2441i, using the same formula for exponential.

IMLN ¶

Calculates the natural logarithm of a complex number.

Purpose: This function is used to compute the natural logarithm of a complex number, commonly used in engineering, physics, and mathematical applications.
Formula: IMLN(inumber)
inumber is the complex number for which you want to calculate the natural logarithm. It can be in the form x+yi or x+yj.
The formula to calculate the natural logarithm of a complex number is:
```
ln(a + bi) = ln|a + bi| + i*arg(a + bi)
```
Where:
- ln|a + bi| is the natural logarithm of the magnitude: ln(sqrt(a² + b²))
- arg(a + bi) is the argument (angle) of the complex number: atan2(b, a)
Example Usage:
=IMLN("1") returns 0, as ln(1) = 0.
=IMLN("i") returns approximately 0 + 1.5708i, as the magnitude is 1 and the angle is π/2 radians.
=IMLN("1+i") returns approximately 0.3466 + 0.7854i, calculated using the formula.
=IMLN("-1-2i") returns approximately 0.8047 - 2.0344i, using the natural logarithm formula.

IMLOG10 ¶

Calculates the base-10 logarithm of a complex number.

Purpose: This function is used to compute the logarithm with base 10 of a complex number, which is useful in engineering, physics, and mathematical applications where log scales are required.
Formula: IMLOG10(inumber)
inumber is the complex number for which you want to calculate the base-10 logarithm. It can be in the form x+yi or x+yj.
The formula for the base-10 logarithm of a complex number is:
```
log10(a + bi) = ln(a + bi) / ln(10)
```
Where ln(10) is the natural logarithm of 10 (approximately 2.3026).
Example Usage:
=IMLOG10("1") returns 0, as log10(1) = 0.
=IMLOG10("10") returns 1, as log10(10) = 1.
=IMLOG10("i") returns approximately 0 + 0.6822i, calculated using the formula.
=IMLOG10("1+i") returns approximately 0.1505 + 0.3411i, using the base-10 logarithm formula.
=IMLOG10("-1-2i") returns approximately 0.3490 - 0.8826i, using the same formula.

IMLOG2 ¶

Calculates the base-2 logarithm of a complex number.

Purpose: This function is used to compute the logarithm with base 2 of a complex number, which is useful in engineering, physics, and mathematical applications involving binary logarithmic scales.
Formula: IMLOG2(inumber)
inumber is the complex number for which you want to calculate the base-2 logarithm. It can be in the form x+yi or x+yj.
The formula for the base-2 logarithm of a complex number is:
```
log2(a + bi) = ln(a + bi) / ln(2)
```
Where ln(2) is the natural logarithm of 2 (approximately 0.6931).
Example Usage:
=IMLOG2("1") returns 0, as log2(1) = 0.
=IMLOG2("2") returns 1, as log2(2) = 1.
=IMLOG2("i") returns approximately 0 + 2.2662i, calculated using the formula.
=IMLOG2("1+i") returns approximately 0.5000 + 1.1331i, using the base-2 logarithm formula.
=IMLOG2("-1-2i") returns approximately 1.1590 - 2.9374i, using the same formula.

IMPOWER ¶

Raises a complex number to a given power.

Purpose: This function is used to calculate the result of raising a complex number to a given power, which is common in engineering, physics, and mathematical applications.
Formula: IMPOWER(inumber, power)
inumber is the complex number that you want to raise to a power. It can be in the form x+yi or x+yj.
power is the power to which the complex number is raised. It can be any real number.
The formula for raising a complex number to a power is:
```
(a + bi)^n = r^n * [cos(n*θ) + i*sin(n*θ)]
```
Where:
- r = sqrt(a² + b²) is the magnitude of the complex number.
- θ = atan2(b, a) is the argument (angle) of the complex number.
Example Usage:
=IMPOWER("1+i", 2) returns 0 + 2i, as (1 + i)^2 = 2i.
=IMPOWER("2", 3) returns 8, as 2^3 = 8.
=IMPOWER("0+i", 4) returns 0, as raising pure imaginary i to the fourth power returns 0 due to cyclic properties of imaginary numbers.
=IMPOWER("-1-2i", 3) returns approximately -11 + 2i, calculated using the power formula.

IMPRODUCT ¶

Calculates the product of two or more complex numbers.

Purpose: This function is used to compute the product of multiple complex numbers, which is widely used in engineering, physics, and mathematical calculations involving complex arithmetic.
Formula: IMPRODUCT(inumber1, [inumber2, ...])
inumber1, inumber2, ... are the complex numbers you want to multiply. Each number can be in the form x+yi or x+yj. At least one number must be provided as input.
The general process for multiplying complex numbers (a+bi) and (c+di) is:
```
(a + bi) * (c + di) = (ac - bd) + (ad + bc)i
```
When multiplying more than two complex numbers, the multiplication is associative, so it proceeds pairwise.
Example Usage:
=IMPRODUCT("1+i", "2+i") returns 1 + 3i, as (1+i) * (2+i) = 1 + 3i.
=IMPRODUCT("2", "3") returns 6, as 2 * 3 = 6.
=IMPRODUCT("1+i", "0") returns 0, since any number multiplied by 0 is 0.
=IMPRODUCT("i", "i") returns -1, as i * i = -1.
=IMPRODUCT("-1-2i", "3+4i") returns 5 - 10i, calculated using the formula for complex multiplication.

IMREAL ¶

Returns the real part of a complex number.

Purpose: This function is used to extract the real part of a given complex number, which is useful in many engineering and mathematical calculations.
Formula: IMREAL(inumber)
inumber is the complex number from which you want to extract the real part. It can be in the form x+yi or x+yj.
The real part of a complex number a + bi is simply a.
Example Usage:
=IMREAL("3+4i") returns 3, as the real part is 3.
=IMREAL("-2") returns -2, as the real part is -2 (no imaginary part present).
=IMREAL("0+i") returns 0, as the real part is 0.
=IMREAL("-1-2i") returns -1, as the real part is -1.
=IMREAL("5") returns 5, as the real part is 5 (no imaginary part present).

IMSEC ¶

Calculates the secant of a complex number.

Purpose: This function computes the secant (1/cosine) of a given complex number, which is useful in engineering, physics, and mathematical applications involving trigonometric functions for complex values.
Formula: IMSEC(inumber)
inumber is the complex number for which you want to calculate the secant. It can be in the form x+yi or x+yj.
The formula for the secant of a complex number is:
```
sec(a + bi) = 1 / cos(a + bi)
```
Where:
- cos(a + bi) = cos(a)cosh(b) - i*sin(a)sinh(b)
- cosh(b) and sinh(b) are the hyperbolic cosine and sine of the imaginary part, respectively.
Example Usage:
=IMSEC("0") returns 1, as sec(0) = 1.
=IMSEC("i") returns approximately 0.6481 - 0.0000i, calculated using the formula.
=IMSEC("1+i") returns approximately 0.4983 - 0.5911i, using the secant formula.
=IMSEC("-1-2i") returns approximately -0.0417 - 0.0903i, calculated using the same formula.

IMSECH ¶

Calculates the hyperbolic secant of a complex number.

Purpose: This function computes the hyperbolic secant (1/cosh) of a given complex number, which is useful in engineering, physics, and mathematical applications involving hyperbolic trigonometric functions for complex values.
Formula: IMSECH(inumber)
inumber is the complex number for which you want to calculate the hyperbolic secant. It can be in the form x+yi or x+yj.
The formula for the hyperbolic secant of a complex number is:
```
sech(a + bi) = 1 / cosh(a + bi)
```
Where:
- cosh(a + bi) = cosh(a)cos(b) + i*sinh(a)sin(b)
- cosh(a) and sinh(a) are the hyperbolic cosine and sine of the real part, respectively.
Example Usage:
=IMSECH("0") returns 1, as sech(0) = 1.
=IMSECH("i") returns approximately 0.6481 + 0.0000i, calculated using the formula.
=IMSECH("1+i") returns approximately 0.4983 - 0.5911i, using the hyperbolic secant formula.
=IMSECH("-1-2i") returns approximately -0.0416 + 0.0903i, calculated using the same formula.

IMSIN ¶

Calculates the sine of a complex number.

Purpose: This function computes the sine of a given complex number, which is useful in engineering, physics, and mathematical applications involving trigonometric functions for complex values.
Formula: IMSIN(inumber)
inumber is the complex number for which you want to calculate the sine. It can be in the form x+yi or x+yj.
The formula for the sine of a complex number is:
```
sin(a + bi) = sin(a)cosh(b) + i*cos(a)sinh(b)
```
Where:
- cosh(b) and sinh(b) are the hyperbolic cosine and sine of the imaginary part, respectively.
Example Usage:
=IMSIN("0") returns 0, as sin(0) = 0.
=IMSIN("i") returns approximately 0.0000 + 1.1752i, calculated using the formula.
=IMSIN("1+i") returns approximately 1.2985 + 0.6349i, using the sine formula.
=IMSIN("-1-2i") returns approximately -3.1658 - 1.9596i, calculated using the same formula.

IMSINH ¶

Calculates the hyperbolic sine of a complex number.

Purpose: This function computes the hyperbolic sine of a given complex number, which is useful in engineering, physics, and mathematical applications involving hyperbolic trigonometric functions for complex values.
Formula: IMSINH(inumber)
inumber is the complex number for which you want to calculate the hyperbolic sine. It can be in the form x+yi or x+yj.
The formula for the hyperbolic sine of a complex number is:
```
sinh(a + bi) = sinh(a)cos(b) + i*cosh(a)sin(b)
```
Where:
- sinh(a) and cosh(a) are the hyperbolic sine and cosine of the real part, respectively.
- cos(b) and sin(b) are the cosine and sine of the imaginary part, respectively.
Example Usage:
=IMSINH("0") returns 0, as sinh(0) = 0.
=IMSINH("i") returns approximately 0.0000 + 0.8415i, calculated using the formula.
=IMSINH("1+i") returns approximately 0.6349 + 1.2985i, using the hyperbolic sine formula.
=IMSINH("-1-2i") returns approximately -1.9596 - 3.1658i, calculated using the same formula.

IMSQRT ¶

Calculates the square root of a complex number.

Purpose: This function computes the square root of a given complex number, which is useful in engineering, physics, and mathematical calculations involving complex numbers.
Formula: IMSQRT(inumber)
inumber is the complex number for which you want to calculate the square root. It can be in the form x+yi or x+yj.
The formula for the square root of a complex number a + bi is:
```
sqrt(a + bi) = ±(sqrt((|a + bi| + a) / 2) + i * sign(b) * sqrt((|a + bi| - a) / 2))
```
Where:
- |a + bi| is the modulus of the complex number, calculated as sqrt(a^2 + b^2).
- sign(b) is 1 if b >= 0, otherwise -1.
Example Usage:
=IMSQRT("4") returns 2, as sqrt(4) = 2.
=IMSQRT("-4") returns 0 + 2i, as the square root of -4 is 2i.
=IMSQRT("3+4i") returns approximately 2 + 1i, calculated using the square root formula.
=IMSQRT("0-1i") returns approximately 0.7071 - 0.7071i, using the same formula.
=IMSQRT("1+i") returns approximately 1.0987 + 0.4551i.

IMSUB ¶

Subtracts one complex number from another.

Purpose: This function computes the difference between two complex numbers, which is useful in engineering, physics, and mathematical calculations involving complex numbers.
Formula: IMSUB(inumber1, inumber2)
inumber1 is the complex number from which you want to subtract another complex number.
inumber2 is the complex number to subtract from inumber1.
The formula for subtracting inumber2 from inumber1 is:
```
(a + bi) - (c + di) = (a - c) + (b - d)i
```
Where:
- a and b are the real and imaginary parts of inumber1, respectively.
- c and d are the real and imaginary parts of inumber2, respectively.
Example Usage:
=IMSUB("3+4i", "1+2i") returns 2 + 2i, as (3 + 4i) - (1 + 2i) = 2 + 2i.
=IMSUB("3+4i", "3+4i") returns 0, as the complex numbers cancel each other out.
=IMSUB("-1+2i", "1-2i") returns -2 + 4i.
=IMSUB("0", "1+i") returns -1 - i, as the subtraction is done directly.

IMSUM ¶

Adds two or more complex numbers.

Purpose: This function computes the sum of two or more complex numbers, which is useful in engineering, physics, and mathematical calculations involving complex numbers.
Formula: IMSUM(inumber1, inumber2, [...])
inumber1, inumber2, [...] are the complex numbers you want to add together. Each number can be in the form x+yi or x+yj.
The formula for adding complex numbers is:
```
(a + bi) + (c + di) + ... + (x + yi) = (a + c + ... + x) + (b + d + ... + y)i
```
Where:
- a, b are the real and imaginary parts of the first complex number, respectively.
- c, d are the real and imaginary parts of the second complex number, respectively.
- x, y are the real and imaginary parts of subsequent complex numbers, respectively.
Example Usage:
=IMSUM("1+2i", "3+4i") returns 4 + 6i, as (1 + 2i) + (3 + 4i) = 4 + 6i.
=IMSUM("0", "1", "1+i") returns 2 + i, as 0 + 1 + (1 + i) = 2 + i.
=IMSUM("-1+2i", "1-2i", "3+4i") returns 3 + 4i, as (-1 + 2i) + (1 - 2i) + (3 + 4i) = 3 + 4i.
=IMSUM("0") returns 0, as it sums to itself when there's only one number.

IMTAN ¶

Calculates the tangent of a complex number.

Purpose: This function computes the tangent of a given complex number, combining real and imaginary parts. It can be applied in various engineering, physics, and mathematical calculations involving complex trigonometric functions.
Formula: IMTAN(inumber)
inumber is the complex number for which you want to calculate the tangent. It can be in the form x+yi or x+yj.
The formula for the tangent of a complex number is:
```
tan(a + bi) = sin(a + bi) / cos(a + bi)
            = (sin(a)cosh(b) + i*cos(a)sinh(b)) / (cos(a)cosh(b) - i*sin(a)sinh(b))
```
Where:
- cosh(b) and sinh(b) are the hyperbolic cosine and sine of the imaginary part, respectively.
- cos(a) and sin(a) are the cosine and sine of the real part, respectively.
Example Usage:
=IMTAN("0") returns 0, as tan(0) = 0.
=IMTAN("i") returns approximately 0.0000 + 1.5574i, calculated using the formula.
=IMTAN("1+i") returns approximately 1.0839 + 0.2718i, using the tangent formula.
=IMTAN("-1-2i") returns approximately 0.0338 - 1.0148i, calculated using the same formula.

O¶

OCT2BIN ¶

Converts an octal number to its binary equivalent.

Purpose: This function converts an octal (base-8) number to a binary (base-2) number. This is useful in programming, electronics, and computer science.
Formula: OCT2BIN(octal_number, [places])
octal_number is the octal number you want to convert to binary. It can be a string or a numeric value.
places (optional) is the number of characters in the result. If the binary result is shorter, leading zeros are added. If omitted, the result uses the minimum number of characters.
Example Usage:
=OCT2BIN("7") returns 111, as 7 in octal is 111 in binary.
=OCT2BIN("10") returns 1000, as 10 (octal) is 1000 in binary.
=OCT2BIN("10", 6) returns 001000, padding with leading zeros to make the result 6 characters long.
=OCT2BIN("377") returns 11111111, as 377 (octal) is 11111111 in binary.
=OCT2BIN("1") returns 1, as 1 in octal is 1 in binary.

OCT2DEC ¶

Converts an octal number to its decimal equivalent.

Purpose: This function converts an octal (base-8) number to a decimal (base-10) number, which is commonly used in various fields like programming, electronics, and computer science.
Formula: OCT2DEC(octal_number)
octal_number is the octal number you want to convert to decimal. It can be a string or a numeric value.
The conversion is calculated as the sum of digits in the octal number multiplied by 8 raised to their positional powers.
Example Usage:
=OCT2DEC("7") returns 7, as 7 in octal is already 7 in decimal.
=OCT2DEC("10") returns 8, as 10 (octal) is 8 in decimal.
=OCT2DEC("377") returns 255, as 377 (octal) is 255 in decimal.
=OCT2DEC("0") returns 0, as 0 in octal is 0 in decimal.

OCT2HEX ¶

Converts an octal number to its hexadecimal equivalent.

Purpose: This function converts an octal (base-8) number to a hexadecimal (base-16) number. It is commonly used in programming, electronics, and computer science.
Formula: OCT2HEX(octal_number, [places])
octal_number is the octal number you want to convert to hexadecimal. It can be a string or a numeric value.
places (optional) is the number of characters in the result. If the hexadecimal result is shorter, leading zeros are added. If omitted, the result uses the minimum number of characters.
The conversion is done by first converting the octal number to decimal, and then converting the decimal number to hexadecimal.
Example Usage:
=OCT2HEX("7") returns 7, as 7 in octal is 7 in hexadecimal.
=OCT2HEX("10") returns 8, as 10 (octal) is 8 in hexadecimal.
=OCT2HEX("377") returns FF, as 377 (octal) is 255 in decimal, and FF in hexadecimal.
=OCT2HEX("10", 4) returns 0008, padding with leading zeros to make the result 4 characters long.
=OCT2HEX("1") returns 1, as 1 in octal is 1 in hexadecimal.