This guide will explain how to use the IMSINH function in Google Sheets.

##### Table of Contents

Complex numbers are formed by adding a real number and an imaginary number. A complex number’s real and imaginary parts define an ordered pair that acts as coordinates in a two-dimensional complex plane.

We often need trigonometric functions when working with complex numbers. If we need to find the hyperbolic sine of a complex number in Google Sheets, we can use the built-in `IMSINH`

function.

In this guide, we will cover each step you need to start using the `IMSINH`

function to calculate the hyperbolic sine of a complex number.

**The Anatomy of the IMSINH Function**

The syntax of the `IMSINH`

function is as follows:

=IMSINH(number)

Let’s look at each argument to understand how to use the `IMSINH`

function.

**number**refers- The number argument can either be a
`COMPLEX`

function result, a real number, or a string in the format “x+yi” where x and y are valid numbers. The`IMSINH`

number can accept any real number since these values are equivalent to a complex number where the imaginary coefficient is zero. - The function will return an error if the number argument is not a valid complex number.
- If you would like to find the sine of a complex number, you should use the
`IMSIN`

function instead.

**The Anatomy of the COMPLEX Function**

The syntax of the `COMPLEX`

function is as follows:

=COMPLEX(real_part, imaginary_part, [suffix])

Let’s look at each argument to understand how to use the `COMPLEX`

function.

**real_part**refers to the real coefficient of the complex number.**imaginary_part**refers to the imaginary coefficient of the complex number**suffix**is an optional argument where the user can indicate the suffix to use for the imaginary coefficient. By default, the value for this argument is “i”.

**A Real Example of Using the IMSINH Function**

Let’s look at a few simple examples where we’ll need to use the `IMSINH`

function in Google Sheets.

### Using a cell reference

We can use the `IMSINH`

function to find the hyperbolic sine given a cell reference as input.

Suppose we have a complex number in cell A2. We can determine the sine using the following formula:

=IMSINH(A2)

In the example above, the `IMSINH`

function shows that the hyperbolic sine of the complex number 3+2i is -4.16890695996656+9.15449914691143i.

### Using the COMPLEX Function

If you are given just the coefficients of a complex number, we’ll need to use the `COMPLEX`

function to generate a valid complex number for `IMSINH`

. For example, the formula **COMPLEX(3,5)** returns the complex number 3+5i.

In the example above, we have a table with the coefficients of our complex numbers’ real and imaginary parts.

We can use the following formula to get the hyperbolic sine given the two coefficients:

=IMSINH(COMPLEX(A2,B2))

Using this formula, we were able to find the hyperbolic sine values given a set of real and imaginary coefficients.

Click on the link below to create your own copy of our examples.

Head to the next section to read our step-by-step tutorial on how to use the IMSINH function.

**How to Use the IMSINH Function in Google Sheets**

- Select the cell where you want to use the
`IMSINH`

function. - Type the
`IMSINH`

function and specify a complex number as the sole argument. You may write down a number in the form “a+bi” or a cell reference to another cell with a valid complex number in that form.

In this example, we’ll use the formula**IMSINH(A2)**to find the hyperbolic sine value of the complex number 3+2i. - Hit the
**Enter**key to evaluate the`IMSINH`

function. - You can use the
**AutoFill**feature to find the hyperbolic sine of the remaining complex numbers in the table. - We can use the
`COMPLEX`

number to convert the coefficients of our complex number into a valid complex number first.

In the table above, we’ll use the formula**IMSINH(COMPLEX(A2,B2))**to find the hyperbolic sine of a complex number with a real part of 3 and an imaginary part of 6.

These are all the steps you need to know to start using the `IMSINH`

function in Google Sheets.

**FAQs**

**Why is my IMSINH function returning an error?**The`IMSINH`

function may output an error if the complex number you’re using as an argument is not in the proper format “a+bi”. If your complex number is missing the imaginary unit suffix, your function may also result in an error.**What is the difference between IMSINH and IMSIN function?**The`IMSINH`

function finds the hyperbolic sine of a complex number, while the`IMSIN`

function calculates the sine of a complex number.

To learn more about using trigonometric functions on complex numbers, you can read our post on how to find the cosine of a complex number in Google Sheets.

That’s all for this guide! Don’t miss out on our library of spreadsheet resources, tips, and tricks!