Use the Cauchy Riemann equations in polar form to show where it is holomorphic.Then use the formula f'(z)=e^{-i theta}[ur+ivr] to show that the derivative is f'(z)=i/z * f(z) 2) Consider the functionf (z = re²) = e cos(In(r)) + ie¯* sin(ln(r)).Show that is holomorphic at all points except the origin. Also show that=

Step 1: The function is: f(z)=e−θcos(ln(r))+ie−θsin(ln(r)) z=re−iθx=∣z∣ , θ=arg(z) Explanation:…

Answered: 2) Consider the function f (z = re²) =…

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

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.6: Additional Trigonometric Graphs

Problem 78E

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Question

Use the Cauchy Riemann equations in polar form to show where it is holomorphic.

Then use the formula f'(z)=e^{-i theta}[u_r+iv_r] to show that the derivative is f'(z)=i/z * f(z)

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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