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The IMAGINARY function in Google Sheets returns the imaginary coefficient of a given complex number. The imaginary coefficient is the part of the complex number that is multiplied by the imaginary unit. This function is often used in engineering and scientific applications that involve complex numbers.


Use the IMAGINARY formula with the syntax shown below, it has 1 required parameter:

  1. complex_number (required):
    The complex number for which to return the imaginary coefficient. The complex number can be supplied as a number, cell reference, or another formula that evaluates to a complex number.


Here are a few example use cases that explain how to use the IMAGINARY formula in Google Sheets.

Calculate the imaginary part of a complex number

The IMAGINARY function can be used to extract the imaginary part of a complex number, which is useful in many engineering and scientific applications.

Calculate the phase angle of a complex number

The phase angle of a complex number can be calculated using the IMAGINARY and REAL functions together in a formula.

Calculate the imaginary coefficient of a range of complex numbers

The IMAGINARY function can be used with an array formula to calculate the imaginary coefficients of a range of complex numbers.

Common Mistakes

IMAGINARY not working? Here are some common mistakes people make when using the IMAGINARY Google Sheets Formula:

Not using a valid complex number format

The parameter for IMAGINARY must be a valid complex number. If you get a #NUM error, check that you are using a valid format for complex numbers, such as 3+4i.

Using a cell reference that does not contain a complex number

If you are referencing a cell that does not contain a complex number, you will get a #VALUE error. Check that the cell you are referencing contains a valid complex number.

The following functions are similar to IMAGINARY or are often used with it in a formula:


    The COMPLEX function returns a complex number based on real and imaginary coefficients. It is commonly used in engineering calculations and signal processing.


    The SUMIF formula is used to add up values in a range that meet a specific criterion. It can be used to sum values based on text, numbers, or dates. The formula is most commonly used in financial analysis, budgeting, and data analysis.


    The PRODUCT formula in Google Sheets multiplies all the numbers given in the arguments and returns the product. It is commonly used to calculate the total product of a range of cells.

Learn More

You can learn more about the IMAGINARY Google Sheets function on Google Support.