# A to Z of Excel Functions: the IMLN Function

5 October 2020

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

**The IMLN 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**.

Sometimes you wish to calculate the natural logarithm of a complex number. The natural logarithm of a complex number is given by

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

**IMLN(inumber)**

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

**inumber:**this is required and represents the complex number for which you wish to calculate the natural logarithm.

It should be further noted that:

- you should use
**COMPLEX**to convert real and imaginary coefficients into a complex number **IMLN**recognises either the**i**or**j**notation- if
**inumber**is a value that is not in the**x + yi**or**x + yj**text format,**IMLN**returns the <>#NUM! error value - if
**inumber**is a logical value,**IMLN**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**IMLN**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. *