How to Use IMSECH Function in Google Sheets

This guide will discuss how to use the IMSECH function in Google Sheets.

When we want to calculate the hyperbolic secant of a complex number, we can easily do this using the IMSECH function.

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

  • The IMSECH function only has one required argument. This is the complex number for which we want the hyperbolic secant.
  • The complex number can be the result of the COMPLEX function, a real number interpreted as a complex number with imaginary parts equal, or a string in the format “a+bi” where a and b are numeric. 
  • If the given number is not a valid complex number, the IMSECH function returns a #NUM! error.
  • 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 a logical value, the IMSECH function returns a #VALUE! error. 

Google Sheets provides dedicated functions that simplify working with complex numbers, making it easier to use them in different situations. This is particularly useful when working in various fields, such as engineering, physics, and mathematics, where we often encounter complex numbers. 

One of these functions is the IMSECH function, which we can use to calculate the hyperbolic secant of a complex number. 

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

Great! Let’s dive right in.

The Anatomy of the IMSECH Function

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

=IMSECH(number)

  • = the equal sign is how we begin any function in Google Sheets.
  • IMSECH() refers to our IMSECH function. This function is used to return the hyperbolic secant of the given complex number. For instance, a complex number a+bi returns sech(a+bi).
  • number is the only required argument. This refers to the complex number for which we want to calculate the hyperbolic secant. This can either be the result of the COMPLEX function, a real number interpreted as a complex number with imaginary parts equal, or a string in the format “a+bi” where a and b are numeric. 

The Anatomy of the COMPLEX Function

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

=COMPLEX(real_part,imaginary_part,[suffix])

  • = the equal sign is how we start any function in Google Sheets.
  • COMPLEX() is our COMPLEX function. This function is used to create a complex number, given real and imaginary coefficients.
  • real_part is a required argument. This refers to the real coefficient we will use in creating the complex number.
  • imaginary_part is another required argument. This refers to the imaginary coefficient we will use in creating the complex number.
  • suffix is an optional argument. This is the suffix we want to use for the imaginary coefficient. By default, the suffix used will be i. 

IMSEC Function vs. IMSECH Function

To use the appropriate function properly, let’s learn the difference between IMSEC and IMSECH functions. The two are similarly spelled, which may cause confusion when not thoroughly checked. 

Both functions are used to calculate mathematical formulas relating to complex numbers. However, the main difference is the output of each function. 

The IMSEC function returns a secant number related to triangles and periodic trigonometric functions. On the other hand, the IMSECH function returns a hyperbolic secant number used in hyperbolas and has applications in various mathematical and physical contexts involving hyperbolic functions.

A Real Example of Using IMSECH Function in Google Sheets

Let’s say we have a data set containing complex numbers. 

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

We want to calculate the hyperbolic secant of the complex numbers. Our initial data set would look like this:

Initial dataset

We can use the formula below to perform our task:

=IMSECH(A2)

IMSECH formula

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. 

Our final data set would look like this:

Final dataset

Let’s say we only have a table with the coefficients of our complex numbers’ real and imaginary parts. The initial data set would look like this:

Initial dataset

In the spreadsheet above, we will utilize the COMPLEX function to create each complex number using the given real and imaginary coefficients. 

Afterward, we can calculate the hyperbolic secant of the complex numbers using the IMSECH function.

To do this, we can use the formula below:

=IMSECH(COMPLEX(A11,B11))

IMSECH and COMPLEX formula

The first part of the formula is the IMSECH function. Remember, the only required argument of the IMSECH function is a complex number which we currently do not have.

That is why for our number argument, we will input the COMPLEX function and select the cells containing the real and imaginary coefficients, which are A2 and B2.

The COMPLEX function will return a complex number using the given coefficient. Then, the IMSECH function will calculate the hyperbolic secant of the created complex number.

Our final data set using the COMPLEX function would look like this:

Final output

You can make your own copy of the spreadsheet above using the link below. 

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

How to Use IMSECH Function in Google Sheets

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

IMSECH Function in Google Sheets

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 “=IMSECH(”.

IMSECH Function in Google Sheets

3. Then, we will simply select the cell containing the complex number. Our final formula would be “=IMSECH(A2)”. We will press the Enter key to return the result.

IMSECH Function in Google Sheets

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

IMSECH Function in Google Sheets

6. Alternatively, we will use the COMPLEX function with our IMSECH function. To do this, we will start with an equal sign and the IMSECH function. Our formula would become “=IMSECH(”.

IMSECH Function in Google Sheets

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

IMSECH Function in Google Sheets

8. Next, we will select the cells containing the real and imaginary coefficients. Our final formula would be “=IMSECH(COMPLEX(A11,B11))”.

IMSECH Function in Google Sheets

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

IMSECH Function in Google Sheets

10. Lastly, we will drag down the Fill Handle tool to apply the formula to the other cells.

IMSECH Function in Google Sheets

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

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

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