# Tagged Questions

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### A question on the 2-norm defined by $||x||_2=\sqrt{\sum\limits_{i=1}^n|x_i|^2}$

A question on the 2-norm defined by $||x||_2=\sqrt{\sum\limits_{i=1}^n|x_i|^2}$ I am trying to prove the triangle inequality of this norm. So far I have that: \begin{align} ...
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### Separating a Complex Valued Function

Is there a formula (with mathematical reasoning) for separating a complex-valued function $f(z)=f(x+iy)$ into the form $f(z)=u(x,y) + iv(x,y)$? Thank You, C.A
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### Finding the types of singularities

I am working on the following: Let $f : \mathbb C \setminus \{1,2\} \to \mathbb C$ be defined by \begin{align*} f(z) = \frac{\sin(z)-2}{z-2} + \frac{\cos(1/(z-2))}{(z-2)^2}+\frac{\cos(z-1)-1}{z-1}. ...
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### Visualizing a complex valued function of one real parameter

I'm looking for a way to capture/graph or visualize it in my head, but I can't find how.. a 2-dimensional path won't do, because it doesn't reveal the rate-of-change.. 2 1-dimensional graphs on top ...
Consider a piecewise differentiable function $f(x):\mathbb{R}\to\mathbb{R}$. Now, analytically continue this function ($x\to z$) to complex argument and values $f(z):\mathbb{C}\to\mathbb{C}$. For such ...