# A to Z of Excel Functions: the IMABS Function

15 June 2020

*Welcome back to our regular A to Z of Excel Functions blog. Today we look at the IMABS function. *

**The IMABS function**

An imaginary number is a complex number that can be written as a real number multiplied by the imaginary unit **i **(sometimes denoted **j**) which is defined by its property **i ^{2}** = −1. In general, the square of an imaginary number

**bi**is

**−b**. For example, 9

^{2}**i**is an imaginary number, and its square is −81. Zero is considered to be both real and imaginary.

An **imaginary** number **bi** can be added to a **rea**l number **a** to form a **complex number** of the form **a + bi**, where the real numbers **a** and **b** are called, respectively, the **real** part and the **imaginary** part of the **complex number**.

Just like the Excel function **ABS** measures the “distance” between a number and zero (0) (*e.g. ***ABS(-5)** is five (5) units from zero (0), therefore, **ABS(-5) **= 5), so **IMABS(“a + bi”)** measures the distance from zero (0) to the point **z = a + bi**. As can be clearly seen in the diagram, this distance is given by Pythagoras’ Theorem

Technically, **IMABS** returns the absolute value, or modulus, of a complex number **a + bi**, provided the number has been provided in said text format.

The **IMABS **function employs the following syntax to operate:

**IMABS(inumber)**

The **IMABS** function has the following argument:

**inumber:**this is required and represents the complex number for which you want the absolute value.

It should be further noted that:

- you should use
**COMPLEX**to convert real and imaginary coefficients into a complex number **IMABS**recognises either the**i**or**j**notation- if the complex number ends in +
**i**or -**i**(or**j**),*i.e.*there is no coefficient between the operator and the imaginary unit, there must be no space, otherwise**IMABS**will return an*#NUM!*error.

Please see my example below:

*We’ll continue our A to Z of Excel Functions soon. Keep checking back – there’s a new blog post every business day.*

*A full page of the function articles can be found here. *