(This is my first post on stackexchange. Please tell me, if I made any formatting errors and such.)
This question is about how the absolute value function works with the complex exponential.
We have to determine, what $|\exp (z^2)|$ is. Since we know that $z=x+i y$ and $|\exp(z)| = \exp(Re(z))$, after some calculation, it arises that $|\exp(z^2)| = \exp(x^2 - y^2)$.
Does the absolute value of the left side of the equation influence the right side? How I take it, since $|\exp(z)| = \exp(Re(z))$ i.e. it doesn't. But as I said, we're unsure.
P.S: Yes, I know that the right side still needs to be calculated further, but right now, I'd primarily like to know, how the abs. value works in this situation.