The IMEXP function in Google Sheets is **useful when you need to raise Euler’s number, also known as ***e***, to a complex power.**

Euler’s number (~2.718) has special properties when raised by an exponent. Using the IMEXP function allows you to raise ** e** to a complex number of the form

*a+bi*.

##### Table of Contents

The rules for using the `IMEXP`

function in Google Sheets are as follows:

- The function requires just one argument. The user must provide the complex number that we will raise e to.
- The function then outputs the result of e raised to that number.
- The formula for raising e to a complex power is as follows: IMEXP(x+yi) = excos(y) + iexsin(y)

Let’s take a look at a quick example!

In this example, we have a spreadsheet with a sample of complex numbers. We would like to return the value of *e *raised to the power of n, where n is a complex number in our sample dataset. Using the `IMEXP`

function, we can easily return the value we are looking for.

Let’s learn how to write the `IMEXP`

function ourselves in Google Sheets and later test out the function to solve the example stated earlier.

**The Anatomy of the IMEXP Function**

So the syntax (the way we write) the `IMEXP`

function is as follows:

=IMEXP(exponent)

Let’s dissect this thing and understand what each of these terms means:

**=**the equal sign is how we start any function in Google Sheets.**IMEXP()**is our`IMEXP`

function. It computes Euler’s number raised to a given complex power.**exponent**refers to our complex power, given in the form*a+bi*.

**A Real Example of Using IMEXP Function**

Let’s look at an example of the `IMEXP`

function being used in a Google Sheet spreadsheet.

In the table below, we have a sample set of complex numbers in Column A. Using the `IMEXP`

function, we’re able to retrieve the values of e raised to each complex number.

To get the values in Column B, we just need to use the following formula:

=IMEXP(A2)

You can make a copy of the spreadsheet above using the link I have attached below.

In another example, we’ve used the same dataset but have also extracted the real and imaginary coefficients.

This is possible thanks to the `IMREAL`

and `IMAGINARY`

functions in Google Sheets, which allow us to retrieve the real and imaginary coefficients of our `IMEXP`

output.

If you’re ready to try out the `IMEXP`

function in Google Sheets, let’s begin writing it ourselves!

**How to Use IMEXP Function in Google Sheets**

- Our guide starts by having an idea of what our inputs are. In the table below, we have our complex numbers placed in Column A. To start using the
`IMEXP`

function, we must first select the cell we would like to contain our output. In this case, we’ll start with cell**B2.**

- Next, we just simply type the equal sign ‘
**=**‘ to begin the function, followed by ‘**IMEXP(**‘. - As seen below, a tooltip box appears with info on the
`IMEXP`

function. We can click on the arrow on the top-right-hand corner of the box to minimize it if necessary.

- Next, we need to provide the cell which contains the complex number we want to use.

Afterward, simply hit**Enter**on your keyboard to let the function evaluate.

- Finally, we can drag down the formula to evaluate our formula for the rest of the dataset.

**Frequently Asked Questions (FAQ)**

**Why does my formula output a #NUM! error?**

A #NUM! error indicates that the complex number provided is invalid. Make sure that the complex number follows the form*a+bi*.**How do I make sure that my number argument is always a valid complex number?**

To make sure that the argument for the`IMEXP`

function is always valid, we can use the COMPLEX function to generate our complex numbers. For example, we can use the formula =COMPLEX(4, 2, ”i”) to create the complex number ‘4 + 2i’.

That’s all you need to know on how to use the `IMEXP`

function in Google Sheets. This step-by-step guide shows how simple it is to raise e to a certain complex power.

You can now use the `IMEXP`

function in Google Sheets with various other formulas available in Google Sheets to create great worksheets that make your work and life easier for you.

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