 Solution

ID: past-exam-of-the-metric-spaces-and-complex-analysis-course-of-the-university-of-oxford/2014/3/c/i/solution

Write

α = a + ib

with

b > 0

. Then

f_{α} (z) = a + b z .

It preserves the upper half-plane, has inverse

(z - a) / b

, and sends

i

α

. Its nonzero derivative

b

verifies that this bijection is conformal.

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