# Tagged Questions

Questions involving complex numbers, that is numbers of the form $a+bi$ where $i^2=-1$ and $a,b\in\mathbb{R}$.

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My younger cousin asked for help on his math homework and I don't remember doing this, can anyone help please? The denominator of $w$ has $z^*+1$ where the $^*$ means to negate the $z$ term so $z^*= ... 3answers 69 views ### Closed form of product of complex numbers [duplicate] I'm stuck in a proof where I want to get a closed form of something. This is the last thing I need to complete my proof: Apparently for small$n\geq2$, the product$\prod\limits_{k=1}^{n-1} ...
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Can somebody please explain $$e^{-\frac{3}{4}\pi i}+e^{-\frac{9}{4}\pi i}+e^{-\frac{15}{4}\pi i}+e^{-\frac{21}{4}\pi i}=0$$ WolframAlpha Computation.
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### Lower bound this expression

The following expression is a logarithmic expression I am trying to put a lower bound on. Assuming $x,y$ are complex variables. $$F=\log \left( 1 + \big||x|-y\big|^2\right)$$ where the notation |.| ...
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### Center of gravity of a regular polygon

How do I prove that the origin is the centroid of the regular polygon whose vertices are the solutions of the equation $z^n=1$ in the complex plane?
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### Real and imaginary part of $(1-i\sqrt{3})^6$

i am a bit stuck here. As the title says i try to find out how to write complex numbers like for example$$(1-i\sqrt{3})^6$$ in the normal representation$$z = x + i*y$$ I already found out that the ...
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### Picard's theorem applied to $f^n + g^n =1$

So I have the following problem. Part 1 is just to state Picard's theorem, so for that we have that any entire holomorphic function takes on every value with possibly one exception. Part 2 is to show ...
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### Prove that $\frac{e^{2x}-1}{e^{2x}+1}i=\tan{ix}$

I have a doubt in complex numbers which I am unable to solve. The question is Prove that $$\left(\frac{e^{2x}-1}{e^{2x}+1}\right)i=\tan{ix}$$ I tried using hyperbolic sin and cosines but failed. Can ...