Problem 1521 (difficulty: 3/10)

Let \(\displaystyle w(z)=\frac 12\left(z+\frac 1z\right)\) be the so called Zhukowksy map. What is the image of

(a) the unit circle? (b) the interior of the unit circle? (c) the exterior of the unit circle?

(d) the circles with center \(\displaystyle 0\)? (e) the lines passing through \(\displaystyle 0\)?

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