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## Homework Statement

What is the mapping of the circle of radius 1 centered at z=-2i

under the mappinf f(z)=1/z

## The Attempt at a Solution

I write the circle in polar form [itex] -2i+e^{ix} [/itex]

Now we invert it and multiply by the complex conjugate.

so we get [itex] f(z)= \frac{2i+e^{-ix}}{5+2i(e^{ix}-e^{-ix})} [/itex]

now sure how to graph it our manipulate it any more, should I break it into real and imaginary parts?

also there was a hint that w=1/z and z=1/w. where w is the complex mapping. any help would be appreciated