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

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-numeric

or

The 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.

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