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

Good to hear from you tboulden!

I found this considerably mentally taxing too and that was without even attempting the recursion that Peter managed. Translating the equations into array operations was enough of an uphill climb in itself!

I was pleased to be able to find the complex number representation above but found care was needed to maintain efficiency, particularly short-circuit evaluation of arguments via IF. I also wanted to add the python code did run successfully when I changed the output, I had just missed initially that the inconsistency was due to reporting amplitudes instead.