Complex Number Functions in Excel

If you do any engineering calculations that involve complex numbers, you’ll probably appreciate the complex number functions that are built into Excel. Excel has many functions for working with complex numbers, but we’ll only cover a few here.

Function Description
COMPLEX Creates a complex number
IMAGINARY Extracts the imaginary coefficient from a complex number
IMREAL Extracts the real coefficient from a complex number
IMDIV Divides complex numbers
IMPRODUCT Multiplies complex numbers
IMSUB Subtracts complex numbers
IMSUM Adds complex numbers

You can browse through the other functions for complex numbers by going to Formulas > More Functions > Engineering. Scroll down to find the functions that begin with “IM.” Hover over each function to get a brief description. You can also see the Excel help for more information.

The COMPLEX function takes real and imaginary coefficients and creates a complex number, either in x+yi or x+yj form. The syntax is as follows:

COMPLEX(real_num, i_num, [suffix])

real_num: the real part of the complex number (x)

i_num: the imaginary part of the complex number (y)

suffix: (optional) suffix for the imaginary part – either “i” (default) or “j”

If you omit the suffix, Excel will use i by default. It’s important to enclose “i” and “j” in double quotation marks in the suffix argument.

The IMAGINARY function can be used to find the imaginary part of an existing complex number – y in x+yi – and returns it to a cell. There’s only one argument for this function – the complex number. The IMREAL function will extract the real part of a complex number (x).

You can’t directly add, subtract, multiply, or divide complex numbers in Excel using symbols (+, -, etc). To perform those operations with complex numbers, you’ll need to use these special functions: IMDIV, IMPRODUCT, IMSUB and IMSUM.

A common example in engineering that uses complex numbers is an AC circuit. In Worksheet 03j, there’s an example that calls for complex number arithmetic:

First, enter in the specified voltage (45+10j) as a complex number. The real part of the voltage is 45 – this will be the first argument. The imaginary part is 10, the second argument. We’ll specify “j” in the third argument so as to not confuse “i” with current. Therefore, the entry for voltage will be =COMPLEX(45,10,”j”). Excel will display this as 45+10j. Do likewise for impedance: =COMPLEX(3,4,”j”).

We need to divide voltage by impedance to find the current, but it’s not possible to simply divide the two complex numbers with the / operator. Use the IMDIV function. This function takes the numerator as its first argument, and the denominator as its second. Therefore, to find the current, enter =IMDIV(C6,C7). Remember to separate the two arguments with a comma, not a slash.

This returns a result of 7-6j for the current.

To learn how to format complex numbers in Excel, check out this post.

To learn how to handle matrix calculations with complex numbers, go here.

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By Charlie Young, P.E.

Take your engineering to the next level with advanced Excel skills.