Complex Analysis: Theory and Applications · Problem 9.1.7

Conformal Mapping — Howell & Matthews

Mathematics — Complex Analysis · conformal-mappings-orthogonal-images

Problem

Consider the mapping w=Log⁡zw = \operatorname{Log} z, where Log⁡z\operatorname{Log} z denotes the principal branch of the logarithm function. Show that the positive xx-axis and the vertical line x=1x = 1 are mapped onto orthogonal curves.

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