Author: Oscar Cronquist Article last updated on September 23, 2022

How to use the <span class='notranslate'>IMABS</span> functionv3

The IMABS function calculates the absolute value (modulus) of a complex number in x + yi or x + yj text format.

A complex number consists of an imaginary number and a real number, complex numbers let you solve polynomial equations using imaginary numbers if no solution is found with real numbers.

1. IMABS Function Syntax

IMABS(inumber)

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2. IMABS Function Arguments

inumber Required. A complex number in x+yi or x+yj text format.

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3. IMABS function example

How to use the <span class='notranslate'>IMABS</span> function

A complex number can be described as z = x + yi or z = x + yj text form in Excel.

The formula to calculate the absolute value z is based on the Pythagorean theorem
z2 = x2+y2

The IMABS function calculates the absolute value using this formula:

IMABS(z) = |z| =√(x2+y2)

x is the real coefficient of the complex number and y is the imaginary coefficient of the complex number.

Formula in cell D3:

=IMABS(C3)

3.1 Explaining formula

Step 1 - Populate arguments

IMABS(inumber)

becomes

IMABS(C3)

Step 2 - Evaluate IMABS function

IMABS(C3)

becomes

IMABS("9+12i")

and returns 15.

Here is how the number 15 is calculated:

z = x + yi

z = 9 + 12i

IMABS(z) = |z| =√(x2+y2)

IMABS(z) = |z| =√(92+122)

IMABS(z) = |z| =√(81+144)

IMABS(z) = |z| =√225

IMABS(z) = |z| =15

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4. How imaginary numbers were invented

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