Solution
= Solution
Multiplication by $i$ is a counterclockwise <rotation> through $\pi/2$: it maps coordinates $(X,Y)$ to $(-Y,X)$. The centre $(2,2)$ therefore becomes $(-2,2)$, and the long axis becomes vertical. For $w=X+iY$, the resulting <ellipse> is
$$
\boxed{\frac{(X+2)^2}{8^2}+\frac{(Y-2)^2}{16^2}=1.}
$$
Its horizontal semiaxis is $8$ and its vertical semiaxis is $16$, as shown in the final panel of the figure in part (b).