Complex Analysis: Theory and Applications · Problem 9.2.4

Conformal Mapping — Howell & Matthews

Mathematics — Complex Analysis · bilinear-transformations

Problem

Show that the bilinear transformation w=i(1−z)1+zw = \dfrac{i(1-z)}{1+z} maps the portion of the disk ∣z∣<1|z| < 1 that lies in the upper half-plane Im⁡(z)>0\operatorname{Im}(z) > 0 onto the first quadrant u>0u > 0, v>0v > 0.

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