# How to Use IMSINH Function in Google Sheets

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

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 to the complex number you want to find the hyperbolic sine of.
• 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

1. Select the cell where you want to use the `IMSINH` function. 2. 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.
3. Hit the Enter key to evaluate the `IMSINH` function. 4. You can use the AutoFill feature to find the hyperbolic sine of the remaining complex numbers in the table. 5. 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

1. 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.
2. 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! Our goal this year is to create lots of rich, bite-sized tutorials for Excel users like you. If you liked this one, you'd love what we are working on! Readers receive early access to new content.

##### You May Also Like ## How to Use YIELD Function in Google Sheets

This guide will explain how to use the YIELD function in Google Sheets. When we need to calculate… ## How To Use FACTDOUBLE Function in Google Sheets

The FACTDOUBLE function in Google Sheets helps you quickly calculate the return of the double factorial of a… ## How to Use the MMULT Function in Google Sheets

The MMULT function in Google Sheets is short for “matrix multiplication function” and it automates row-to-column multiplication for… ## How to Replace Blank Cells with Zero in Google Sheets

The Find and Replace function is useful when you need to replace blank cells in your Google Sheets…  