List questions from complex-numbers

Published on 15 Apr 2026 - 9:15

300

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Find the sum of the series $\sum_{k=1}^\infty \frac{\cos 2kx}{k^2}$

Published on 13 Apr 2026 - 21:34

57

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How to solve for complex expression?

Published on 08 Apr 2026 - 19:58

97

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Prove that $\alpha=\beta=\gamma$ where $\alpha,\beta, \gamma$ are complex numbers.

Published on 16 Apr 2026 - 7:33

267

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Problem about the upper bound of the modulus of a root of a monic polynomial

Published on 11 Apr 2026 - 23:57

44

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Prove equilateral triangle if vertices $a,b,c$ satisfy $|a|=|b|=|c|$ and $\sum_{cyc}\frac1{8-a/b-b/a-a/c-c/a}=0.3$

Published on 16 Apr 2026 - 10:45

102

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A problem regarding complex variable equation $sz+t\bar{z}+r=0$

Published on 11 Apr 2026 - 7:18

116

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Showing that a power series is convergent and finding radius of convergence

Published on 14 Apr 2026 - 2:59

69

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Complex number inequality $\left|\sum_{k=1}^n\Im(z^k)\right| < \sqrt{\frac{1}{2}\Re\left(n-\sum_{k=1}^n\frac{z^{2k}}{|z|^{2k}}\right)}$

Published on 16 Apr 2026 - 4:46

70

Views

Find expression for following summation

Published on 05 May 2026 - 3:26

47

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Problems solving a Complex exponential equation

Published on 12 Apr 2026 - 0:36

177

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Complex natural logarithms by hand

Published on 19 Apr 2026 - 0:46

194

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Cauchy's integral formula, application

Published on 12 Apr 2026 - 22:35

83

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$z^2 = -1$ Why what i do is wrong?

Published on 11 Apr 2026 - 6:14

42

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Imaginary part of $f(z)$

Published on 15 Apr 2026 - 19:54

List Question

Simplifying ${\left| {1 - \bar zw} \right|^2} - {\left| {z - w} \right|^2}$

Find the sum of the series $\sum_{k=1}^\infty \frac{\cos 2kx}{k^2}$

How to solve for complex expression?

Prove that $\alpha=\beta=\gamma$ where $\alpha,\beta, \gamma$ are complex numbers.

Problem about the upper bound of the modulus of a root of a monic polynomial

Prove equilateral triangle if vertices $a,b,c$ satisfy $|a|=|b|=|c|$ and $\sum_{cyc}\frac1{8-a/b-b/a-a/c-c/a}=0.3$

A problem regarding complex variable equation $sz+t\bar{z}+r=0$

Showing that a power series is convergent and finding radius of convergence

Complex number inequality $\left|\sum_{k=1}^n\Im(z^k)\right| < \sqrt{\frac{1}{2}\Re\left(n-\sum_{k=1}^n\frac{z^{2k}}{|z|^{2k}}\right)}$

Find expression for following summation

Problems solving a Complex exponential equation

Complex natural logarithms by hand

Cauchy's integral formula, application

$z^2 = -1$ Why what i do is wrong?

Imaginary part of $f(z)$

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