# Tagged Questions

The theory of functions of one complex variable with an emphasis on the theory of complex analytic (or holomorphic) functions of one complex variable. Typical topics include: Cauchy's integral formula, singularities, poles, meromorphic functions, Laurent and Taylor series, maximum modulus principle, ...

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### Differentiability complex functions

If u, v : Ω → C are C^1 functions in an open set Ω ⊂ C, and f = u + iv. Then if the Cauchy–Riemann equations is not satisfied at any points of Ω, does it mean that f is not differentiable?
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### Complex Analysis - Write in x+iy form

Write ($\frac{\sqrt{2}}{(i-1)})^{10}$ in $x+iy$ form. I'm completely stuck and cannot figure it out. Can someone please walk me through the solution?
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### Solving a functional equation in complex analysis

Is there any simple (general) way to find the complex solution of a functional-equation? For example, it is given $f(z) = f\big(\frac{z^2+4}{3}\big)$, and the question is to find all the ...
### What is the value of $x^{n}$ when $x\in\Bbb N$ and $n\in\Bbb C$? [duplicate]
How can I calculate $x^{n}$ when $x\in\Bbb N$ and $n\in\Bbb C$ ? Respectively $x^{ni}$