# The Excel COMPLEX Function

Complex Numbers

Within the world of complex numbers, the 'imaginary' value, i is used to represent the square root of -1.

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

## Function 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 syntax 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 text argument, equal to "i" or "j" that specifies the suffix to be used. I.e. whether the imaginary number is written in the style 5+2i or 5+2j. If omitted, the [suffix] argument uses the default value "i".

## Excel Complex Function Examples

The following spreadsheets show the Excel Complex function, used to create different complex numbers.

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
1 5+2i
2 5-9i
3 -1+2j
4 10-5i
5 5i
6 3

Further examples of the Excel Complex function are provided on the Microsoft Office website.

## Complex Function Error

If you get an error from your Excel Complex function this is likely to be the #VALUE! error:

Common Error
 #VALUE! - Occurs if either: One or both of the supplied real_num or i_num arguments are non-numeric or The supplied [suffix] argument is something other than "i" or "j".