# The Excel COMPLEX Function

Complex Numbers

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 :

√(-4)   =   2i

A Complex Number is composed of a real number combined with an imaginary number.

E.g. The complex number, z, is written as

z   =   5 + 2i

## Basic Description

The Excel Complex function takes two arguments, representing the real and the imaginary coefficients of a complex number, and from these, creates a complex number.

The format of the function is :

COMPLEX( real_num, i_num, [suffix] )

where the arguments are as shown in the table below:

 real_num - The real component of the complex number i_num - The imaginary component of the complex number [suffix] - An optional argument that is used to specify a suffix to be used.(For example, if we want the imaginary number 5+2i to use the suffix "j" (i.e. to be written as 5+2j), we would set the [suffix] argument to "j")If supplied, the [suffix] argument, must be equal to either "i" or "j";If omitted, this argument takes on the default value "i"

## Excel Complex Function Examples

In the examples below, the Complex function is used to create different complex numbers in Excel.

Formulas:
A
1=COMPLEX( 5, 2 )
2=COMPLEX( 5, -9 )
3=COMPLEX( -1, 2, "j" )
4=COMPLEX( 10, -5, "i" )
5=COMPLEX( 0, 5 )
6=COMPLEX( 3, 0 )
Results:
A
15+2i
25-9i
3-1+2j
410-5i
55i
63

Further examples of the Excel Complex function can be found on the Microsoft Office website.

## Complex Function Common Errors

If you get an error from your Excel Complex function this is likely to be one of the following :

Common Errors
 #VALUE! - Occurs if either:One or both of the supplied real_num or i_num arguments are non-numericorThe supplied [suffix] argument is something other than "i" or "j" #NAME? - Occurs when Analysis ToolPak add-in is not enabled in your Excel.You will need to enable the add-in if you want to use the Excel complex number functions.