Related Function:

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

### Syntax

=IMAGINARY(inumber)

#### Arguments

Argument Description
inumber A complex number for which you want the imaginary coefficient. The inumber argument can be supplied to the IMAGINARY function as either:

 • a simple number • a complex number encased in quotation marks, e.g. “5+3i” • a reference to a cell containing a complex number or a numeric value • a value returned from another function or formula

Note: Use the COMPLEX function to convert real and imaginary coefficients into a complex number.

#### Examples

A B C D
1 Data Formula Result Notes
2 3+4i =IMAGINARY(A2) 4 Imaginary coefficient of the complex number 3+4i
3   =IMAGINARY(“3+4i”) 4
4   =IMAGINARY(“2-i”) -1
5   =IMAGINARY( COMPLEX(4,1)) 1

#### Common Function Error(s)

Problem What went wrong
#NUM! Occurs if the supplied inumber argument is not recognized as a complex number
#NAME? Occurs when Analysis ToolPak add-in is not enabled

Within the real number scale, there is no such thing as the square root of a negative number. However, within the world of complex numbers, the ‘imaginary’ value, i is used to represent the square root of -1.

Therefore, the square root of any negative number can be represented by the square root of the number’s modulus, multiplied by i.

For example:

Complex Number is composed of a real number combined with an imaginary number, e.g. the complex number, z, is written as: