# A to Z of Excel Functions: the IMPOWER Function

26 October 2020

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

**The IMPOWER function**

This function is kind of **IMPOWER**ing…

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**.

Sometimes you might wish to raise a complex number to a power. **IMPOWER **returns a complex number that is in the **x + yi** or **x + yj** text format to a given power.

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

**IMPOWER(inumber, number)**

The **IMPOWER** function has the following arguments:

**inumber:**this is required and represents the complex number you wish to raise to a power**number:**this is also required. This is the power to which you wish to raise the complex number.

It should be further noted that:

- you should use
**COMPLEX**to convert real and imaginary coefficients into a complex number **IMPOWER**recognises either the**i**or**j**notation- if
**inumber**is a value that is not in the**x + yi**or**x + yj**text format,**IMPOWER**returns the*#NUM!*error value - if
**inumber**is a logical value,**IMPOWER**returns the*#VALUE!*error value - if
**number**is non-numeric,**IMPOWER**returns the*#VALUE!*error value - 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**IMPOWER**will return an*#NUM!*error - a complex raised to a power is calculated as follows:

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. *