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.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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.)
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