Is it generally true that a map is conformal at points where $f'(z)\neq 0$, why? (I saw this argument used in Kapoor's Complex Variables) And Kapoor alse seems to suggest that we can determine the magnification of the angle by finding the smallest $n$ where $f^{(n)}(z)\neq 0$. My suspicion is that it probably has something to do with Taylor expansion of the map?
Is this generally true? On an argument regarding conformal maps
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complex-analysis
taylor-expansion
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0Study a map $f(z) = az$ near $z=0$ when $a \ne 0$. Then study the difference between that map and a map with Taylor series $az + \dots$. – 2012-02-01