Show analytically (finding the centre and radius) that $z(t)=\frac{1}{(1-i)^{-1}-t}=\frac{2}{1+i-2t}$ where $z(t)\in C $, that $z(t)$ traces out a circle in the complex plane as $t$ is varied.
Circle in the complex plane
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complex-analysis
circles
complex-geometry