Complex numbers in Excel

I see it is a while since this was first posted.

I have used complex numbers but, in the main prefer to implement it using pairs of floating point numbers rather than relying upon Microsoft's text-based implementation.  Many years ago I implemented spectral analysis calculations based upon the Bretschneider spectrum

representing sea state in the North Atlantic.  My reason for using tables of real numbers was mainly to control the number formatting of both the real and imaginary parts to show 4 decimal places rather than varying length strings.  A creative application that does not really have anything to do with complex numbers is to split a range held as text using

Back to more serious matters, LAMBDA and recursion turn the Excel formula into a Turing complete programming language.  Rather than plunging into the theory to back up that assertion, I chose to demonstrate it by programming a truly horrendous problem based upon the complex roots of unity, namely to implement a fast Fourier transformation (FFT).  This time I used arrays of complex numbers held as real number pairs, not because of appearance, but rather to achieve the necessary performance.