 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/ii/paper-1/24f/b/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

Log z = lo g ∣ z ∣ + i ar g z

, with

- π < ar g z < π

. Then

f (z) = i Log z = - ar g z + i lo g ∣ z ∣

is a conformal equivalence from the slit plane to the vertical strip. Its imaginary part tends to

- \infty

z \to 0

and to

+ \infty

z \to \infty

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