MAT334--2020F > Quiz 3

Quiz3-5E

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Qiaoyi Zhang:
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 ${|w|}<1$