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## Homework Statement

Find the image of the circle |z| = 3 in the complex plane under the mapping

a) w = [itex]\frac{6}{z}[/itex]

b) w = [itex]\frac{6}{z}[/itex] + 2i

## The Attempt at a Solution

a) w = [itex]\frac{6}{3}[/itex] = 2

So this is a circle in the w-plane of radius 2, centered on the origin?

b) w = [itex]\frac{6}{3}[/itex] + 2i

So this is a line in the w-plane extending from the origin to the point 2 + 2i ?

I'm not entirely sure of how this works, is w an absolute? like |w| = 2?