# How to Use IMTANH Function in Google Sheets

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

When we need to calculate the inverse hyperbolic tangent of a complex number, we can easily do this using the `IMTANH` function in Google Sheets.

The rules for using the `IMTANH` function in Google Sheets are the following:

• A complex number must be in the format “a+bi” or “a-bi”, where a and b are real numbers and i is the imaginary unit.
• If the given number is not a valid complex number, the `IMTANH` function returns an error.
• When calculating the hyperbolic tangent of multiple complex numbers, we can use the `ARRAYFORMULA function` together with the `IMTANH` function.
• The `IMTANH` function returns a complex number as a result.
• When inputting the number argument, we must always enclose the number in quotation marks to make it a string.

Google Sheets has a wide-range of built-in functions that let us accurately perform many difficult tasks. It provides dedicated functions that simplify working with complex numbers, making it easier to use them in different situations.

One of these functions is the `IMTANH` function, which we can use to calculate the hyperbolic tangent of a complex number.

This is particularly useful when working in various fields such as engineering, physics, and mathematics, where we often encounter complex numbers.

In this guide, we will provide a step-by-step tutorial on how to use the `IMTANH` function in Google Sheets. Additionally, we will explore the syntax and a real example of using the function.

Great! Let’s dive right in.

## The Anatomy of the IMTANH Function

The syntax or the way we write the `IMTANH` function is as follows:

`=IMTANH(number)`

• = the equal sign is how we begin any function in Google Sheets.
• IMTANH() refers to our `IMTANH` function. This function is used to return the hyperbolic tangent of the given complex number. For instance, a given complex number a+bi returns tanh(a+bi).
• number is the only required argument. This refers to the complex number we want to return to the hyperbolic tangent. The value can be either a string in the format “a+bi” where a and b are numeric or the result of the COMPLEX function.

Note: The COMPLEX function creates a complex number, given real and imaginary coefficients.

## The Anatomy of the ARRAYFORMULA Function

The syntax or the way we write the `ARRAYFORMULA` function is as follows:

`=ARRAYFORMULA(array_formula)`

• = the equal sign is how we activate any function in Google Sheets.
• ARRAYFORMULA() refers to our `ARRAYFORMULA` function. This function enables the display of values returned from an array formula into multiple rows and/or columns and the use of non-array functions with arrays.
• array_formula is the only required argument. This refers to a range, a mathematical expression using one cell or multiple ranges of the same size, or a function that returns a result greater than one cell.

Note: You can also press Ctrl+Shift+Enter while editing a formula to automatically add ARRAYFORMULA( to the beginning of the formula.

## Common Mistakes in Using IMTANH Function

The `IMTANH` function has a straightforward syntax making it simple to use. However, we still need to be careful when using some things to ensure the function properly works.

Firstly, we may have entered the complex number in an incorrect format. We must make sure to use the format a+bi or a-bi, where a and b are real numbers and i is the imaginary unit.

Moreover, remember to input the complex number in quotation marks when entering the number directly into the formula to make it a string.

Secondly, we may have used the wrong function for the desired calculation. The `IMTANH` function is used to calculate the inverse hyperbolic tangent of a complex number.

If we want to calculate the regular tangent of a complex number, we must utilize the `IMTAN` function.

Lastly, check the syntax of the formula. Ensure the syntax of the function call is correct, including the proper placement of commas, the use of parentheses, and the quotation marks for the complex number.

## A Real Example of Using IMTANH Function in Google Sheets

Let’s say we have a data set containing complex numbers. We want to calculate the inverse hyperbolic tangent of the complex numbers. Our initial data set would look like this:

Complex numbers show the numbers that consist of a real part and an imaginary part, represented as a +bi, where a and b are real numbers, and i is an imaginary unit.

In this example, we want to calculate the inverse hyperbolic tangent of the complex numbers in the data set. We can easily complete this task using the `IMTANH` function.

We will use the formula below to perform our task:

`=IMTANH(A2)`

The formula only has one argument, which refers to the complex number we want to calculate. In this case, we simply selected the cell A2 containing the complex number.

If we want to input the complex number directly in the formula, we must enclose it in quotation marks to make it a string value. For instance, we will type “4+5i”.

In the spreadsheet above, we have multiple complex numbers we want to calculate. We can insert the `ARRAYFORMULA function` at the beginning of our formula to easily calculate the hyperbolic tangent of multiple complex numbers.

Our formula would become:

`=ARRAYFORMULA(IMTANH(A2:A8))`

In this formula, we selected the entire range containing the complex numbers. The `ARRAYFORMULA` function will apply the `IMTANH` function to each cell in the range.

Thus, the formula will calculate the inverse hyperbolic tangent of the complex numbers and return an array of the results.

Both formulas would yield the same final data set:

Amazing! Now we can dive into the steps of using the `IMTANH` function in Google Sheets.

## How to Use IMTANH Function in Google Sheets

1. First, we will create a new column in the data set to display inverse hyperbolic tangents of the complex numbers.

2. We will select the first empty row to type in our formula. To start, we will type in an equal sign and the function name. Our formula would be “=IMTANH(”.

3. Then, we will simply select the cell containing the complex number. Our final formula would be “=IMTANH(A2)”.

4. We will press the Enter key to return the result.

5. Next, we will drag down the Fill Handle tool to copy the formula to the other cells.

6. Alternatively, we can apply the `ARRAYFORMULA` function to our `IMTANH` function. To do this, we will start with an equal sign and the `ARRAYFORMULA` function. Our formula would become “=ARRAYFORMULA(”.

7. Then, we will type in the `IMTANH` function. In this case, our formula would become “=ARRAYFORMULA(IMTANH(”.

8. Next, we will select the entire range containing the complex numbers. Our final formula would become “=ARRAYFORMULA(IMTANH(A2:A8))”.

9. We will press the Enter key to return the array.

And tada! We have successfully used the `IMTANH` function in Google Sheets.

You can apply this guide whenever you need to calculate the inverse hyperbolic tangent of a complex number. You can now use the `IMTANH` function and the various other Google Sheets formulas available to create great worksheets that work for you.

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