[Math] Specifying complex domain in Wolfram Alpha

Question

Hopefully this kind of question is ok, have seen a couple of other WA-queries that hasn't been downvoted. Apologies if not.

I'm trying to find the max/min of a complex function over certain domains, the unit disk or circle for example. It doesn't seem as though Wolfram Alpha understands what I'm trying to say though.

For example if I try $4z^2 +1, |z|=1$, WA just ignores the absolute value restriction. I've tried mod(z), abs(z), $\{|z|=1\}$ and some other stuff. Documentation only seems to contain examples over the reals. Any guesses?

Answer 1

Optimization problems generally assume real input an output. Accordingly, WolframAlpha assumes this type of input. You can get around this issue by recasting your problem in terms of real real variables. For example:

minimize |4 (x + I*y)^2 + 1| for x^2+y^2==1

or

minimize |4*exp(I*t) + 1|