How to Calculate Complex Numbers in Excel

Performing calculations on complex numbers in Excel is not difficult because Excel has a set of functions that allow many different calculations of complex numbers.

Complex numbers consist of a real part and an imaginary part. You can perform arithmetic operations on complex numbers. Excel has built-in functions that will make it easier for you to perform complex calculations.

You can use a spreadsheet to perform operations with complex numbers. To use the complex number functions, you must first install the Analysis Toolpak.

The functions that enable this are included in the group of engineering functions. Below we present the most important of them.

Wherever the argument is a complex number, enter it in the form “a + bi” or “a + bj”, where i and j denote the imaginary unit. This form can also be obtained in place of the argument by inserting the formula COMPLEX (a; b; “i”) or COMPLEX (a; b; “j”).

How to sum complex numbers

Use the IMSUM function to sum complex numbers. The syntax for the IMSUM function is = IMSUM (inumber1, inumber2, …). You must enter a minimum of two complex numbers that you want to add together.

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sum of complex numbers

The formula for adding complex numbers in my example is =IMSUM(B3,C3).

Complex number subtraction

Use the IMSUB function to find the difference of complex numbers. The syntax for the IMSUB function is =IMSUB(inumber1, inumber2, …).

subtraction of complex numbers

The IMSUB formula I used: =IMSUB(B3,C3).

How to find the product of complex numbers

Use the IMPRODUCT function to find the product of complex numbers.

product of complex numbers

In my case, the formula product to =IMPRODUCT(B3, C3) i gave the result 2 + 62i.

How to find the quotient of complex numbers

Use the IMDIV function to find the quotient of complex numbers. The imdiv function returns the quotient of two complex numbers.

quotient of complex numbers

In my case, the formula quotient is =IMDIV(B3, C3).

How to find the absolute value of a complex number

Use the IMABS function to find the modulus of a complex number. The imabs function returns the absolute value of a complex number.

absolute value of complex number

In my case, the formula imabs is =IMABS(B3).

How to find the argument of a complex number

To find the argument of a complex number, use the IMARGUMENT function. The imargument function returns the argument q of a complex number expressed in radians.

argument of complex number

In my case, the formula imabs is =IMARGUMENT(B3).

How to find the conjugate of a complex number

Use the IMCONJUGATE function to find the conjugate of a complex number. The imargument function returns the conjugate of a complex number.

conjugate of complex number

In my case, the formula for imconjugate is =IMCONJUGATE(B3).

IMPOWER (team_number, integer_number) – returns a complex number raised to the power of a given integer.

How to find the natural logarithm of a complex number

Use the IMLN function to find the natural logarithm of a complex number. The imargument function returns the natural logarithm of a complex number.

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natural logarithm of complex number

In my case, the formula imln is =IMLN(B3).

Likewise, you can also calculate:

  • base-10 logarithm of a complex number using the IMLOG10 function
  • base-2 logarithm of a complex number using the IMLOG2 function

How to find the square root of a complex number

Use the IMSQRT function to find the square root of a complex number. The imargument function returns the exp of a complex number.

square root of complex number

In my case, the formula imexp is =IMSQRT(B3).

How to find the exponential of a complex number

In order to find the exponents of a complex number use the IMEXP function. The imargument function returns the exp of a complex number.

exponent of complex number

In my case, the formula imexp is =IMEXP(B3).

Hope the Excel tutorial of complex number calculator above helped you. I believe that thanks to this knowledge, no complex number calculations will be difficult for you.