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2) Consider the function f (z = re²) = e cos(In(r)) + ie¯* sin(ln(r)). Show that is holomorphic at all points except the origin. Also show that =

2) Consider the function f (z = re²) = e cos(In(r)) + ie¯* sin(ln(r)). Show that is holomorphic at all points except the origin. Also show that =

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 78E
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Use the Cauchy Riemann equations (polar form version).

Also, describe what happens at the branch cut.

2) Consider the function f (z = re²) = e cos(In(r)) + ie¯* sin(ln(r)). Show that is holomorphic at all points except the origin. Also show that =
Transcribed Image Text:2) Consider the function f (z = re²) = e cos(In(r)) + ie¯* sin(ln(r)). Show that is holomorphic at all points except the origin. Also show that =
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