Author: Oscar Cronquist Article last updated on May 23, 2023

How to use the IMABS function 1

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. It has applications in engineering such as electronics, electromagnetism, signal analysis, and more.

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 IMABS function 1

The IMABS function calculates the modulus of a complex number, IMABS probably stands for imaginary absolute. The absolute value is the same as the modulus.

The modulus of a complex number is the distance of the complex number from the origin in the complex plane. It is the square root of the sum of the squares of the real part and the imaginary part of the complex number. If the complex number is Z then the modulus is denoted |Z|.

The image above shows a chart of the complex plane, complex number 9+12i is the blue line ending with an arrow. The complex plane has an imaginary axis and a real axis, the dashed circle shows the modulus value when it crosses both the imaginary axis and the real axis.

Formula:

=IMABS(C26)

The formula calculates the modulus based on the value in cell C26 which is "9+12i" in this example. The formula returns 15 which the dashed circle also shows when it crosses the imaginary and real axis. Section 4 below explains in greater detail how the IMABS function calculates the modulus.

The modulus is needed when you want to:

3.1 Explaining formula

Step 1 - Populate arguments

IMABS(inumber)

becomes

IMABS(C26)

Step 2 - Evaluate IMABS function

IMABS(C26)

becomes

IMABS("9+12i")

and returns 15.

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4. How is the modulus calculated in detail?

How to use the IMABS function calculate modulus

The formula to calculate the absolute value or modulus z from a complex number is based on the Pythagorean theorem.

z2 = x2+y2

The IMABS function calculates the absolute value using this formula which is based on the Pythagorean theorem:

IMABS(z) = |z| =√(x2+y2)

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

The modulus of a complex number is how far it is from the point where the real and imaginary axes cross (0,0). It is the square root of the real part squared plus the imaginary part squared.

Here is how the modulus is calculated for complex number 9+12i:

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

5. How imaginary numbers were invented

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