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Verify that f(z) = ln r + i0, –T < 0 < T satisfies the Cauchy-Riemann equa tions in polar coordinates. Here, z + 0 has polar coordinates (r, 0). (This f(z is the complex logarithm.)

Verify that f(z) = ln r + i0, –T < 0 < T satisfies the Cauchy-Riemann equa tions in polar coordinates. Here, z + 0 has polar coordinates (r, 0). (This f(z is the complex logarithm.)

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.5: Applications Of Inner Product Spaces
Problem 91E
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Verify that f(z) = ln r + iθ, −π < θ < π satisfies the Cauchy-Riemann equations in polar coordinates. Here, z 6= 0 has polar coordinates (r, θ). (This f(z)
is the complex logarithm.)

Verify that f(2) = In r + i0, –T <0 < T satisfies the Cauchy-Riemann equa- tions in polar coordinates. Here, z +0 has polar coordinates (r, 0). (This f(2) is the complex logarithm.)
Transcribed Image Text:Verify that f(2) = In r + i0, –T <0 < T satisfies the Cauchy-Riemann equa- tions in polar coordinates. Here, z +0 has polar coordinates (r, 0). (This f(2) is the complex logarithm.)
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