Toronto Math Forum
MAT3342020F => MAT334Tests and Quizzes => Quiz 3 => Topic started by: Qiaoyi Zhang on October 09, 2020, 01:31:41 PM

Show that the function $w=g(z)=e^{z^2}$ maps the lines ${x=y}$ and ${x=y}$ onto the circle ${w}=1$. Show further that g maps each of the two pieces of the region $\{x+iy: x^2>y^2\}$ onto ${w}>1$ and $\{x+iy: x^2<y^2\}$ onto ${w}<1$