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IMAGINARY Function

Excel 2007+, Excel 2010+, Excel 2013+, Excel 2016+, Excel 2019+, Excel 365+

Summary

The Excel IMAGINARY function extracts the imaginary coefficient from a complex number expressed in x + yi or x + yj format. It returns the 'y' value from a complex number, making it essential for complex number arithmetic and engineering calculations.

Syntax

IMAGINARY(inumber)

Parameters

Parameter	Type	Required	Description
inumber	`Complex`	Yes	The complex number from which to extract the imaginary coefficient

Using the IMAGINARY Function

IMAGINARY is a key function for working with complex numbers in Excel, particularly useful in engineering, physics, and mathematics where calculations involve both real and imaginary components. Pair it with REAL and COMPLEX functions for full complex number manipulation.

Common IMAGINARY Examples

Extract Imaginary Coefficient from Text Complex Number

=IMAGINARY("3+4i")

Returns 4, the imaginary part of 3+4i

Handle Negative Imaginary with j Notation

=IMAGINARY("0-j")

Returns -1 for the complex number 0-j

Pure Real Number Handling

=IMAGINARY(4)

Returns 0 since 4 is purely real (4+0i)

Frequently Asked Questions

Accepts complex numbers in 'x+yi' or 'x+yj' text format, or pure real numbers which return 0.

IMAGINARY extracts the imaginary coefficient (y), while REAL extracts the real coefficient (x).

Yes, use COMPLEX(real_num, imag_num) to create complex numbers, then IMAGINARY to extract the imaginary part.

Common Errors and Solutions

#VALUE! error

Cause: Invalid complex number format

Solution: Use proper 'x+yi' or 'x+yj' format. Check for correct + or - signs.

#NUM! error

Cause: Input cannot be interpreted as complex number

Solution: Ensure input follows complex number syntax rules

Notes

IMAGINARY returns 0 for purely real numbers
Supports both i and j imaginary unit notation
Use COMPLEX function to build complex numbers from separate real/imaginary parts
Available since Excel 2007 across all modern versions

Compatibility

Available in: Excel 2007, Excel 2010, Excel 2013, Excel 2016, Excel 2019, Excel 2021, Microsoft 365

Not available in: Excel 2003 and earlier

Content last reviewed: December 9, 2025
Update frequency: As needed
Excel versions tested: Excel 2007+, Excel 2010+, Excel 2013+, Excel 2016+, Excel 2019+, Excel 365+