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if a complex function $f$ is real-differentiable, then $f$ or $\overline{f}$ are complex-differentiable This is an exercise from Remmert's Theory of Complex functions.  Let $D\subset \mathbb{C}$ be a domain and $f:D\rightarrow \mathbb{C}$ a real-differentiable function. Assume that the following limit exists:  $ \mathrm{lim}_{h\rightarrow 0} \left|  \frac{f(c+h) - f(c)}{h}   \right|.$  Show that either $f$ or $\overline{f}$ is complex-differentiable.  I've tried showing that $\frac{\partial f}{\partial \overline{z}} = 0$ or $\frac{\partial \overline{f}}{\partial z} = 0$ by using the fact that there exist continuous functions $g$ and $h$ such that in $D$ one can write   $f(z) = f(c) + (z-c)g(z) + (\overline{z} - \overline{c})h(z)$   and that  $g(c)= f_{z}(c)$ and $h(c) = f_{\overline{z}}$ and then plugging this into the limit above. Does this approach works and I just can´t see how to do it? Can someone give a hint or a guideline solution to this? A book on quantum mechanics supported by the high-level mathematics In Python, what's the difference between 'except Exception as e' and 'except Exception, e' I'm looking for a way to reinterpret an array of type byte[] as a different type, say short[]. In C++ this would be achieved by a simple cast but in C# I haven't found a way to achieve this without resorting to duplicating the entire buffer.  Any ideas? I'm about to fly from Istanbul to Seoul and I have a useful amount of Turkish Lira (TRY) left but I don't have any South Korean Won (KRW) to pay for the metro to my hostel when I get there.  Several times in the past I've ended up being stuck with currencies that are very difficult to exchange in the country I've arrived in.  Can I buy KRW at the airport in Istanbul?  (I've also asked , since Stack Exchange questions are meant more for the long tail than just for the original asker.) I have found that the question I want to ask someone had asked, here is the website:    Here is my question: Why $\dim(\hom(V,W))=\dim V * \dim W $?    Thanks for explanation~! "There are no comments" vs. "There is no comment" Are there any options of bash with which it is invoked? I  that the default shell that I use when I start Terminal (with Ctrl+Alt+T) is /bin/bash.   And running the built-in command  on  as:   type -p bash   returns the result as:  /bin/bash   Suggesting the same executable is run when I do Ctrl+Alt+T or say bash.  This shell is the same as an invocation of the command  with some of its options passed to it right? If yes, what are these options?   As an example, perhaps the -i option gets passed so as to make the bash shell interactive?   PS: Maybe  is related too, but I cannot seem to piece together all the pieces here. My keyboard has no "media" keys; can I control media without them? How to run scripts every 5 seconds? What is the geometric meaning of the determinant of a matrix? I know that "The determinant of a matrix represents the area of ​​a rectangle." Perhaps this phrase is imprecise, but I would like to know something more, please.  Thank you very much. The complex general linear group is a subgroup of the group of real matrices of twice the dimension and with positive determinant.  Let us decompose complex matrices $M$ as $M=A+iB$, where $A,B$ are real matrices. Now consider the correspondence $$f(A+iB)=\begin{pmatrix} A &amp; -B \\ B &amp; A\end{pmatrix}.$$  If $\det f(M)=|\det M|^2$ for square matrices, then we would have $GL(n,\mathbb C)\subseteq GL_+(2n,\mathbb R)$ with the identification $M\to f(M)$, which is an injective homomorphism. In other words, the complex general linear group would be a subgroup of the group of real matrices of twice the dimension and with positive determinant.  How is $\det f(M)=|\det M|^2$? Present or Past tense to describe a past condition which is still present? Scenario: My friend John has a personality disorder, intensely paranoid for example.  Can I say:     There were three events last year that told me John had a problem.   or can I say:     There were threee events last year that told me John has a problem. I wanted a list of sub-domains of Stack Exchange that are not mentioned over here   Some of the sub-domains I found which were not mentioned are       Are there any other which are not mentioned?    Mentions by , ,             Other mentions below which are not mentioned in "All Sites" but are mentioned in the drop down menu on the top left of the Stack Exchange website         Any other website that's left out ? ClassNotFoundException: org.eclipse.jetty.util.component.AbstractLifeCycle running inside jetty Speed of light in a gravitational field? How do I solve the speed of light in gravitational field?  Should I just add gravitational acceleration in speed of light?  $$c'=c_0+g(r)t~?$$ How can I render an edge only mesh as solid lines? Prediction interval for binomial random variable I have two internet connection from two different ISP. ADSL on eth0 and 4G on wlan0. Is there any way that if one ISP fails, the other take over automatically without a physical router and by Host OS (Ubuntu 18.04)? Failed to mount Windows share: Invalid argument