Purpose
Return value
Syntax
=IMAGINARY(inumber)- inumber - The string representing a complex number.
Using the IMAGINARY function
The Excel IMAGINARY function returns the imaginary part of a complex number. For example:
=IMAGINARY("4+3i") // returns 3
Excel handles complex numbers as strings formatted like "x+yi" or "x+yj". Use the COMPLEX function to get the string representing a complex number.
Explanation
A complex number is drawn as an arrow in the complex plane, where the horizontal axis corresponds to the real part of the number and the vertical axis corresponds to the imaginary part of the number. For example, the complex number "2-5i" is drawn below.
The IMAGINARY function returns the vertical component of the complex number.
=IMAGINARY("2-5i") // returns -5
Notes:
- IMAGINARY returns a #NUM error when the input does not represent a valid complex number.
Images courtesy of wumbo.net.
Related functions
COMPLEX Function
The Excel COMPLEX function returns the string representation of a complex number.
IMREAL Function
The Excel IMREAL function returns the real part of a complex number.
IMABS Function
The Excel IMABS function returns the absolute value of a complex number.
IMARGUMENT Function
The Excel IMARGUMENT function returns the angle of a complex number expressed in radians. The argument, also known as the phase, is the angle between the positive real axis and the line the complex number lies on in the complex plane.
