Parameterize $ \left| z - 2 \right| = 1 $.

Question

Parameterize $$ \left| z - 2 \right| = 1. $$

I know that the answer should be $$ z(t) = 2 + e^{it}. $$

But I don't know how to do this. And no, I haven't triend anything since I don't know where to start.

Answer 1

The circle $|z|=1$ has parameterization $z=e^{it}$, $0 \le t \le 2\pi$. Thus the circle $|z-2| = 1$ has parameterization $z-2 = e^{it}$, $0 \le t \le 2\pi$.

Answer 2

Hint : The equation represents a circle. convert the following into an eqaution of circle by taking $z=x+iy$ and see how you can parametrize it.