Would you recommend the use of Excel complex numbers where performance is required?

Excel is now meant to be Turing complete so it appears to be possible to write serious computing functionality.  As an experiment,  I have implemented a Discrete Fourier Transformation algorithm using recursive FFT.  I avoided the built-in text-based functionality to process complex numbers and instead wrote a Lambda function to replace complex multiplication

Multiplyλ

= LET(
    u, TAKE(w, ,  1),
    v, TAKE(w, , -1),
    x, TAKE(z, ,  1),
    y, TAKE(z, , -1),
    HSTACK(u * x - v * y, u * y + v * x)
  )

I allowed each complex number of the array to spill across two columns, but was it necessary?

For anyone who might be interested, the solution I presented uses a double recursion to navigate a tree of calculations (typically this is used to reduce 10 000 000 multiplications to a mere 50 000, but I am not planning to try that with Excel)

DFTλ(z, N, s)

= IF( N = 1, z,
    LET(
        z₀, DFTλ(Splitλ(z, 2, 0), N / 2, 2 * s),
        z₁, DFTλ(Splitλ(z, 2, 1), N / 2, 2 * s),
        W,  TAKE(Splitλ(W₀, N₀ / N), N / 2),
        p,  z₀,
        q,  Multiplyλ(W, z₁),
        VSTACK(p + q, p - q)
    )
  )

The key element of the function DFTλ is that it calls itself twice, first following a branch of the calculation until it goes full depth; it evaluates that and then backs up a level and calculates the other branch.  The final part of the routine combines two results before moving back up a further level.

I agree I haven't exactly followed the spreadsheet mantra for formula of 'keep it simple', but someone has to try it!

# Lambda functions

# Recursion

# Complex Numbers