Skip to content

Im sum

IMSUM Function

The IMSUM function in Excel adds two or more complex numbers. This function is commonly used in engineering, mathematical, and scientific fields where operations on complex numbers are needed.

Key Features of IMSUM:

  • Performs addition between two or more complex numbers expressed in the form a+bi or a+bj.
  • Handles real numbers by treating them as complex numbers with an imaginary part of 0.
  • Returns the result in a valid complex number format.

Syntax:

IMSUM(inumber1, [inumber2], ...)
  • inumber1: The first complex number or real number to be added. This can be:
    • A string, such as "6+4i".
    • A cell reference containing a valid complex number.
    • A real number.
  • inumber2, ...: Additional complex numbers or real numbers to add. Same input formats as inumber1.

Formula Details:

Adding complex numbers involves summing their real and imaginary parts separately. For two complex numbers z1 = x1 + y1i and z2 = x2 + y2i, the sum is:

z = (x1 + x2) + (y1 + y2)i

Excel automates this calculation and formats the result as a complex number.

Examples:

  1. Adding Two Complex Numbers:
    =IMSUM("5+3i", "2-4i")
    Adds 5 + 3i and 2 - 4i:
    Result: 7 - i

  2. Adding Real Number and Complex Number:
    =IMSUM(10, "3+5i")
    Treats 10 as 10 + 0i and adds to 3 + 5i:
    Result: 13 + 5i

  3. Adding Multiple Complex Numbers:
    =IMSUM("1+2i", "3+4i", "5-6i")
    Adds the three numbers:
    Result: 9 + 0i

  4. Using Cell References:
    If cell A1 contains "4+3i" and cell A2 contains "5-7i", then:
    =IMSUM(A1, A2)
    Adds 4 + 3i and 5 - 7i:
    Result: 9 - 4i

  5. Handling Purely Real Numbers:
    =IMSUM(6, 4)
    Adds 6 and 4, both treated as real numbers:
    Result: 10 + 0i

  6. Adding Imaginary Numbers:
    =IMSUM("0+4i", "0-3i")
    Adds 4i and -3i:
    Result: 0 + i

Notes:

  • If any input is not formatted as a valid complex number, Excel will return a #VALUE! error.
  • The output is always displayed in complex number format, even if the imaginary part is 0 (e.g., 4 is displayed as 4+0i).

Applications:

  • Engineering: Useful for adding impedance or phasors in circuit analysis.
  • Mathematics: Simplifies operations on complex numbers in algebraic equations.
  • Science: Helps solve complex systems and models involving imaginary components.
  • IMSUB: Subtracts one complex number from another.
    Example: =IMSUB("7+3i", "4+5i") → 3 - 2i
  • IMPRODUCT: Multiplies two or more complex numbers.
    Example: =IMPRODUCT("1+2i", "3-4i") → 11 + 2i
  • IMDIV: Divides one complex number by another.
    Example: =IMDIV("6+8i", "3-2i") → 0.153846154 + 2.692307692i
  • IMSQRT: Finds the square root of a complex number.
    Example: =IMSQRT("4+3i") → 2 + 0.75i

Summary:

The IMSUM function in Excel provides a straightforward and efficient way to add complex numbers. This functionality is essential in applications that require arithmetic with real and imaginary components, ensuring accurate computation in various fields.