# Toronto Math Forum

## MAT334--2020F => MAT334--Tests and Quizzes => Quiz 3 => Topic started by: Qiaoyi Zhang on October 09, 2020, 01:31:41 PM

Title: Quiz3-5E
Post 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 ${|w|}<1$