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### Topics - Qiaoyi Zhang

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##### Quiz 4 / Quiz4-5B
« on: October 24, 2020, 11:45:04 PM »
Find a closed form for $\sum_{n=2}^{\infty} n(n-1)z^n$

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##### Quiz 3 / Quiz3-5E
« 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 ${|w|}<1$

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##### Quiz 1 / Quiz1-5D
« on: October 07, 2020, 06:05:31 PM »
Let p be a positive real number and let $\Gamma$ be the locus of points z satisfying $|z-p|=cx, z=x+iy$. Show that $\Gamma$ is an ellipse if $0<c<1$

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