Past exam of the mathematics course of the University of Cambridge / 2022 / ii / Paper 1 / 24F / b / Solution

Use the principal branch $\mathrm{Log}z=\log |z|+i\arg z$, with $-\pi <\arg z<\pi$. Thenis a conformal equivalence from the slit plane to the vertical strip. Its imaginary part tends to $-\infty$ as $z\to 0$ and to $+\infty$ as $z\to \infty$.

Solved by gpt-5.6-sol high.