The COMPLEX function converts real and imaginary coefficients into a complex number of the form x + yi or x + yj.

Syntax

=COMPLEX(real_num,i_num,[suffix])

Arguments

Argument Description
real_num The real coefficient of the complex number
i_num The imaginary coefficient of the complex number
[suffix] Optional. The suffix for the imaginary component of the complex number

 • If supplied, the [suffix] argument must be equal to either “i” or “j” • If omitted, the [suffix] argument defaults to value “i”

Examples

A B C
1 Formula Result Notes
2 =COMPLEX(3,4) 3+4i Complex number with 3 and 4 as the real and imaginary coefficients
3 =COMPLEX(3,4,”j”) 3+4j Complex number with 3 and 4 as the real and imaginary coefficients, and j as the [suffix]
4 =COMPLEX(0,1) i Complex number with 0 and 1 as the real and imaginary coefficients
5 =COMPLEX(1,0) 1 Complex number with 1 and 0 as the real and imaginary coefficients

Common Function Error(s)

Problem What went wrong
#VALUE! Occurs if either:

 • one or both of the supplied real_num or i_num arguments are non-numeric • the supplied [suffix] argument is something other than “i” or “j”
#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: