How to Use the IMSIN Function in Google Sheets

This guide will explain how to use the IMSIN Function in Google Sheets

Complex numbers are defined as a combination of a real number and an imaginary number. A complex number’s real and imaginary parts make up an ordered pair that works as coordinates in a two-dimensional complex plane.

Since we’re operating on two dimensions, we often need trigonometric functions when working with complex numbers. If we need to find the sine of a complex number in Google Sheets, we can use the built-in IMSIN function.

In this guide, we will cover each step you need to start using the IMSIN function to calculate the sine of a complex number.

The Anatomy of the IMSIN Function

The syntax of the IMSIN function is as follows:

=IMSIN(number)

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

• number refers to the number for which you want to find the sine.
• 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 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 IMSIN Function

Let’s explore a few simple examples where we’ll need to use the IMSIN function in Google Sheets.

Using a cell reference

We can use the IMSIN function to find the 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:

=IMSIN(A2)

In the example above, we used the IMSIN function and found that the sine of the complex number 3+2i is 0.53092108624852-3.59056458998578i.

Using the COMPLEX function

If only the coefficients of the complex number are given, we’ll need to use the COMPLEX function to produce a valid complex number for the IMSIN 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 sine given the two coefficients:

=IMSIN(COMPLEX(A2,B2))

Using this formula, we were able to find the 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 start using the IMSIN function in Google Sheets.

How to Use the IMSIN Function in Google Sheets

1. Select the cell where you want to output the sine.
   
2. Type the IMSIN function and add the target 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 IMSIN(A2) to find the sine value of the complex number 3+2i.
   
3. Hit the Enter key to evaluate the IMSIN function.
   
4. Use the AutoFill feature to find the sine result of the remaining complex numbers in the dataset.
   
5. When given the coefficients of the complex number, use the COMPLEX function to output a valid complex number.
   In our table above, we’ll use the formula IMSIN(COMPLEX(A2,B2)). The COMPLEX function is used inside the IMSIN function to convert the coefficients 3 and 2 into the valid complex number 3+2i.

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

FAQs

1. Why is my IMSIN function returning an error?
   The IMSIN function may return an error for a variety of reasons.  Ensure that the complex number you’re using as an argument is in the proper format a+bi. If your complex number is missing the imaginary unit suffix, your function may result in an error.
   
2. How do I find the other trigonometric functions given a complex number?
   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 IMTAN function to find the tangent of a complex number.

To learn more about using Google Sheets to work with complex numbers, you can read our guide 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!