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complex analysis - Calculating $\int\frac {e^ {iz}} {z}\, dz$ on the . . .
As a part of an exercise I need to calculate $$ \\lim_{r\\to0}\\int_{\\sigma_{r}}\\frac{e^{iz}}{z}\\, dz $$ Where $$ \\sigma_{r}:\\,[0,\\pi]\\to\\mathbb{C
The complex function $\\log(1+e^{iz})$ - Mathematics Stack Exchange
I'm not sure what you mean by circumnavigating the poles rather than taking the Cauchy principal value To me that sounds like the same thing, which would seemingly show that the imaginary part of $\log (1+e^ {iz})$ is not bounded just above real axis with that choice of branch cut I'm sorry for being a bit dumb here
complex analysis - If $e^ {i\bar {z}}=e^ {iz}$ then $x=n\pi . . .
I'm not sure the problem is stated correctly Take $z=1$ (or any real number) Then $e^i=e^i$
Why is $2\pi$ the period of $e^ {iz}$? - Mathematics Stack Exchange
The argument of $e^ {i z}$ is $z$, so it's $z$ that's shifted by $2\pi$ (not $iz$) So you should be considering $e^ {i (z+2\pi)}$ not $e^ {i z+2\pi}$
Integrating $ (e^ {iz}-1) z$ about a semi-circle to evaluate Dirichlet . . .
An exercise in the second chapter of Stein-Shakarchi's Complex Analysis, asks us to evaluate the famous integral $$\\int^{\\infty}_{0}\\frac{\\sin(x)}{x}dx=\\frac
Number of solutions of $z^5+4z^3=e^ {iz}$ in $A=\ {z:1 lt; |z| lt; 3\}. $
So we need the number of solutions in an this annulus and we will use Rouche's theorem Let $p(z)=z^5+4z^3-e^{iz}$ We will first find the number of zeros in $D[0,3
Complex analysis : If $z =re^ {i\theta}$, then prove that $|e^ {iz}| =e . . .
In the title of your problem, instead of $|e^ {i\theta}|$ you meant $|e^ {iz}|$, didn't you?

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