How to Use the IMSEC Function in Google Sheets

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

Complex numbers are created by combining numbers in the traditional number line with imaginary numbers. A complex number’s real and imaginary parts form an ordered pair that can be used as coordinates in a two-dimensional complex plane.

Complex numbers are useful in a variety of fields, including engineering and physics. Since working with complex numbers involves using a 2-D plane, trigonometric functions are often used on complex numbers to calculate certain values.

We can use the IMSEC function in Google Sheets to find the secant of a complex number. In this guide, we will provide a step-by-step tutorial on how to start using the IMSEC function to calculate the secant of a complex number.

The Anatomy of the IMSEC Function

The syntax of the IMSEC function is as follows:

=IMSEC(number)

Let’s look at each argument to understand how to use the IMSEC function.

• number refers to the number for which you want to find the secant.
• The number argument can either be the result of the COMPLEX function, a real number, or a string in the format “x+yi” where x and y are valid numbers.
• the function will return an error if the number argument is not a valid complex number.

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 IMSEC Function

Let’s explore a few simple examples of using the IMSEC function in Google Sheets.

Using a cell reference

Given a cell reference, we can use the IMSEC function to find the secant of the value contained in that cell reference.

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

=IMSEC(A2)

In the example above, we used the IMSEC function and found that the secant of the complex number 3+2i is -0.263512975158389+0.0362116365587685i.

Using the COMPLEX Function

For cases where only the coefficients of the complex number are given, we’ll need to use the COMPLEX function to generate a valid complex number for the IMSEC function.

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 secant given the two coefficients:

=IMSEC(COMPLEX(A2,B2))

Using the COMPLEX and IMSEC functions together, we were able to find the secant of a complex number given the 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 using the IMSEC function in Google Sheets.

How to Use the IMSEC Function in Google Sheets

1. Select the cell where you want to place the result of the IMSEC function.
   
2. Enter the IMSEC function and add a complex number as an argument. You can either write down a complex number written in the form “a+bi” or a cell reference to a valid complex number.
   In this example, we’ll use the formula IMSEC(A2) to find the secant value of the complex number 3+2i.
   
3. Hit the Enter key to evaluate the IMSEC function.
   
4. Use the AutoFill feature to find the secants of the remaining complex numbers in the column.
   
5. If you’re given the coefficients of the complex number, we’ll need to use the COMPLEX function to generate a valid complex number.
   In the example above, we’ll use the formula IMSEC(COMPLEX(A2,B2)). The COMPLEX function is used inside the IMSEC function to convert the coefficients 3 and 2 into 3+2i.

These steps are all you need to know to start using the IMSEC function in Google Sheets.

FAQs

1. Why is the IMSEC function returning an error?
   The IMSEC function may return an error for a variety of reasons. First,  ensure that the complex number you’re using as an argument is in the proper format. If your complex number is missing the imaginary unit “i”, your function may result in an error.
   
2. How do I find the other trigonometric functions given a complex number?
   Besides IMSEC, Google Sheets includes several other functions to help you perform trigonometric functions on complex numbers. You can use the IMCOS function to find the cosine of a complex number and the IMSIN function to find the sine of a complex number.
   If you wish to find the hyperbolic secant instead of the secant, you can use the IMSECH function instead.

To learn more about using Google Sheets to work with complex numbers, you can read our post on how to find the natural logarithm of a complex number.

That’s all for this guide! Be sure to check out our library of spreadsheet resources, tips, and tricks!