Summary

IMAGINARY returns the imaginary coefficient of a complex number. If a cell contains a value like 3+4i, IMAGINARY gives you just the imaginary side, which is 4.

This is useful when a worksheet stores values as full complex numbers but the next step only needs the imaginary part. Instead of pulling that piece out by hand, you can let Excel return it directly.

Syntax

=IMAGINARY(inumber)

inumber is the complex value you want to read.

The input can be a complex number typed directly as text, a cell that contains a complex number, or the result of a function such as COMPLEX(). IMAGINARY then returns only the imaginary coefficient as a normal number.

Arguments

• inumber - [required] The complex number you want to read the imaginary part from.

inumber needs to be in a valid Excel complex-number format such as 3+4i or 3+4j. Plain real numbers are also allowed, and in that case the result is 0 because there is no imaginary part to extract. Using COMPLEX() is often the safest way to create valid input.

IMAGINARY vs similar functions

IMAGINARY is for reading one part of a complex value, not creating or combining one:

Using IMAGINARY

The main use is straightforward. If a cell holds a complex value but your next formula only needs the imaginary side, IMAGINARY saves you from splitting or cleaning the text yourself. That keeps the worksheet easier to read and easier to maintain.

Microsoft also shows that shorthand forms are handled for you. A value like 0-j returns -1, and a plain real number like 4 returns 0 because there is no imaginary part. In the same way, j or i is treated as a coefficient of 1.

Excel accepts complex values written with either i or j. That helps when you are working with engineering-style notation, but the input still has to be a valid complex number format or Excel will return an error.

Example 1 - Extract the imaginary part from 3+4i

This example shows the main purpose of IMAGINARY: isolate the coefficient attached to the imaginary unit and return it as a normal number. The formula strips away the real component and leaves only the imaginary coefficient, which is often the part needed for follow-up calculations.

=IMAGINARY("3+4i") // Returns 4

Example 2 - Read the imaginary part from 50+30j

The same extraction works with j-notation, which is common in engineering models. Excel reads the complex value correctly and returns 30 as the imaginary coefficient. That makes the function reliable across both accepted suffix styles.

=IMAGINARY("50+30j") // Returns 30

Example 3 - Keep a negative imaginary value

The returned value keeps the original sign of the imaginary coefficient. In this case, IMAGINARY returns -5, which is important when the sign reflects direction, phase orientation, or another meaningful engineering distinction.

=IMAGINARY("10-5i") // Returns -5

Example 4 - Read a unit imaginary value

Shorthand complex notation still works here. A plain j means an imaginary coefficient of 1, so IMAGINARY returns 1. This is useful because it shows Excel understands compact complex notation rather than requiring the coefficient to be written explicitly every time.

=IMAGINARY("j") // Returns 1

Quick recap

• Returns the imaginary part: IMAGINARY pulls only the imaginary side out of a complex value.
• Returns a number: The result is ready for normal formulas.
• Keeps the sign: Negative imaginary values stay negative.
• Handles shorthand: i or j is treated as 1, and 0-j returns -1.
• Returns 0 for real input: If there is no imaginary part, the result is zero.
• Works with i or j: Both are valid when the input is a proper Excel complex value.