Complex Analysis: Theory and Applications · Problem 9.4.12

Applications of Harmonic Functions — Howell & Matthews

Mathematics — Complex Analysis · trigonometric-mapping-exercise

Problem

Find the image of the right half-plane Re⁡(z)>0\operatorname{Re}(z) > 0 under the mapping w=Arctan⁡(z)=i2Log⁡ ⁣(i+zi−z).w = \operatorname{Arctan}(z) = \frac{i}{2}\operatorname{Log}\!\left(\frac{i+z}{i-z}\right).

Browse the problem library