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Excel IMAGINARY function

Author: Siluvia Last Modified: 2022-04-13

The IMAGINARY function returns the imaginary coefficient of a given complex number in the form x + yi or x + yj.

Note: A complex number is composed of a real coefficient and an imaginary coefficient. You can apply the COMPLEX function to convert real and imaginary coefficients to a complex number of the form x + yi or x + yj.




  • Inumber (required): The complex number for which you want to return the imaginary coefficient.


1. The argument can be supplied as any of the following:
-- A real number whose imaginary part is 0, e.g., 1 is a complex number 1+0i; Or a purely imaginary number whose real part is 0, e.g., i is a complex number 0 + 1i;
-- A cell reference that refers to a complex number;
-- A complex number enclosed in double quotation marks.
2. The #VALUE! error occurs if “inumber” is a logical value.
3. The #NUM! error occurs if “inumber” cannot be recognized as a complex number.

Return value

It returns a numeric value.


In the following table, there is a list of complex numbers. To get the imaginary coefficients of these complex numbers, you can apply the IMAGINARY function as follows to get it done.

Select a cell (says D6 in this case), enter the formula below and press the Enter key to get the first imaginary coefficient. Select this result cell and then drag its AutoFill Handle down to get other results.



1) The complex number can be directly entered into the formula and needs to be enclosed in double quotation marks. So, the formula in D6 can be changed to:


2) The IMAGINARY function accepts only lowercase “i” and “j”.

Related Functions

Excel COMPLEX function
The COMPLEX function converts real and imaginary coefficients to a complex number of the form x + yi or x + yj.

Excel IMABS function
The IMABS function gets the absolute value of a complex number in the form x + yi or x + yj.

Excel impower function
The IMPOWER function returns a complex number raised to a given power.

Excel improduct Function
The IMPRODUCT function returns the product of 1 to 255 complex numbers in x + yi or x + yj text format.

Excel BITAND function
The IMREAL function returns the real coefficient of a complex number in the form x + yi or x + yj.

Excel IMSUB function
The IMSUB function returns the difference of two complex numbers in x + yi or x + yj text format.

Excel IMSUM function
The IMSUM function returns the sum of two or more complex numbers in x + yi or x + yj text format.

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