Show that C is a circle and find its radius and centre.

Let $z=it$ where $t$ is a real number we get $$w=\frac{1}{1+it} = \frac{1}{1+t^2}-\frac{it}{1+t^2}$$

With $$x= \frac{1}{1+t^2}$$ and $$y=-\frac{t}{1+t^2}$$ we have $$x^2 + y^2 = x$$ which is a circle with center at $\big(\frac{1}{2}, 0\big)$ and radius of $\frac{1}{2}.$

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Complex Numbers

Solution Verification

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