Question
Using polar coordinates (Problem 46), find out whether the following functions satisfy the Cauchy-Riemann equations.$$\ln z$$
Step 1
The function is $\ln z$, where $z$ can be expressed in polar coordinates as $re^{i\theta}$. So, we have: $$ \ln z = \ln(re^{i\theta}) = \ln r + \ln(e^{i\theta}) $$ Show more…
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