Solution
= Solution
For $z=e^{i\theta}$ the image is $w=2\cos\theta$, a real number. Therefore \b[each semicircle maps onto the real interval $[-2,2]$], with endpoints included for closed semicircles. Under positive traversal of the full unit <circle>, the upper half runs from $2$ to $-2$ and the lower half returns from $-2$ to $2$. Every interior point has two unit-circle preimages. The <Joukowski circle-to-ellipse mapping> degenerates to a doubled line segment at this radius.