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# A to Z of Excel Functions: The COMPLEX Function

15 September 2017

Welcome back to our regular A to Z of Excel Functions blog.  Today we look at the COMPLEX function.

The COMPLEX function

Imagine this complex function.  This function converts real and imaginary coefficients into a complex number of the form x + yi or x + yj, where i or j denotes the square root of -1.

The COMPLEX function employs the following syntax to operate:

COMPLEX(real_num, i_num, [suffix])

The COMPLEX function has the following arguments:

• real_num: this is required and represents the real coefficient of the complex number
• i_num: this is also required. This denotes the imaginary coefficient of the complex number
• suffix: this argument is optional. The suffix for the imaginary component of the complex number. If omitted, suffix is assumed to be "i".

NOTE: All complex number functions accept "i" and "j" for suffix, but neither "I" nor "J". Using uppercase results in the #VALUE! error value, given the possible confusion with cell references etc. All functions that accept two or more complex numbers require that all suffices match.

It should be further noted that:

• if real_num is non-numeric, COMPLEX returns the #VALUE! error value
• if i_num is non-numeric, COMPLEX returns the #VALUE! error value
• if suffix is neither "i" nor "j", COMPLEX returns the #VALUE! error value
• arithmetic operations involving imaginary numbers require specific functions such as IMSUB (subtract), IMSUM (add), IMPRODUCT (multiply) and IMDIV (divide). If these are not used, the calculations will return the #VALUE! error value.