# Specifying complex domain in Wolfram Alpha

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?

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"min 4z^2+1 with |z|=1" seems to work – zarathustra Jan 5 '14 at 8:44
If $z \in \mathbb C$, then what does it mean to ask for the "maximum" of $4z^2 + 1$? $\mathbb C$ is not an ordered field. – heropup Jan 5 '14 at 8:49
Good point but I think it's clearly implied that it's the maximum of the modulus we're looking for. Antoine's suggestion worked fine! Although strictly speaking, I guess min |4z^2 +1| with |z|=1 would be more correct. – Benjamin Lindqvist Jan 5 '14 at 8:58
"min |4z^2+1| with |z|=1" indicates that the minimum is 5, yet $|4i^2+1|=3$, which is less than 5. Thus, it seems that WA is assuming the input is real. – Mark McClure Jan 5 '14 at 14:38

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

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