Problem 1522 (difficulty: 3/10)

Sketch the set of those complex number for which

(a) \(\displaystyle \displaystyle\left|\frac{z-1}{z+1}\right|=1\);  (b) \(\displaystyle \displaystyle\left|\frac{z-1}{z+1}\right|=2\);  (c) \(\displaystyle \displaystyle\arg(z+1)=\arg(2z-1)\)  (\(\displaystyle -\pi<\arg z\le\pi\)).

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