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Q3]a)Describe arctanh(z) in terms of logarithms. c) Find derivative of arctanh(z).

Q3]a)Describe arctanh(z) in terms of logarithms. c) Find derivative of arctanh(z).

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.5: Polar Coordinates
Problem 98E
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Q3]a)Describe arctanh(z) in terms of logarithms. c) Find derivative of arctanh(z). Q4] A complex function in term of polar coordinates, (r, ) is described as f(z)=u(r,0)+j v(r,0). The Cauchy-Riemann equations in polar coordinates are 1 dv ar ди dv 1ди %3D r d0 ar And the Laplace equation in polar equation in polar coordinates is 1 a2ø r or ' r2 a02 1 дФ %3D ar2 By employing these equations, show that Ø(r,0)=°cos(20) is harmonic and obtain harmonic conjugate, v(r,0) of u(r,0). The auxiliary of the harmonic conjugate is v (0,0) =0. HUAWEI Nova 2 Plus DUAL CAMERA
Transcribed Image Text:Q3]a)Describe arctanh(z) in terms of logarithms. c) Find derivative of arctanh(z). Q4] A complex function in term of polar coordinates, (r, ) is described as f(z)=u(r,0)+j v(r,0). The Cauchy-Riemann equations in polar coordinates are 1 dv ar ди dv 1ди %3D r d0 ar And the Laplace equation in polar equation in polar coordinates is 1 a2ø r or ' r2 a02 1 дФ %3D ar2 By employing these equations, show that Ø(r,0)=°cos(20) is harmonic and obtain harmonic conjugate, v(r,0) of u(r,0). The auxiliary of the harmonic conjugate is v (0,0) =0. HUAWEI Nova 2 Plus DUAL CAMERA
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