Aug 23, 2016 · This ultimately means that complex differentiable functions send little circles to little circles (a rotation and scaling surely does just this), which for one thing explains why complex differentiable functions are conformal, which in turn helps explain why they are …

Mar 18, 2017 · I would say your easiest option is to learn how to rewrite complex functions as parametrics as Henry hinted at and use a standard graphing utility. $\endgroup$ – Dando18 Commented Mar 17, 2017 at 23:55

Oct 5, 2014 · For the fourth equality, where the FTOC is supposed to be used, I'm not sure how to parse it. The FTOC that I know is for functions $:\mathbb{R} \rightarrow \mathbb{R}$. Any hints, insight, or more detail are very much appreciated.

Sep 22, 2015 · Spivak, Ch. 26, "Complex Functions": Understanding comments about differentiability of complex-valued functions. Hot Network Questions Words with at least 8 letters which have multiple occurrences of the same letter but not consecutively

Apr 6, 2018 · First book: Theory of Complex Functions, Reinhold Remmert. This book does not assume real analysis, only mathematical analysis is sufficient. The author gives a concise introduction in complex analysis, but there are only a few exercises available in the book.

L'Hopital's rule is a local statement: it concerns the behavior of functions near a particular point. The global issues (multivaluedness, branch cuts) are irrelevant.

I just wanted to point out that I wrote a Python package, cplot, that makes plotting complex-valued functions fairly simple. It combines domain coloring and contour lines for constant arg/abs. e.g., for $\sin(z)/z$:

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$\begingroup$ If you're interested, you are heartly welcome to post this example on: Complex Mean Value Theorem: Counterexamples $\endgroup$ – C-star-W-star Commented Dec 8, 2014 at 16:38

I am currently reading Hamming's Numerical Methods for Scientists and Engineers.On pg. 79 he discusses the topic of finding the zeros of a complex analytic function.