List questions from complex-analysis

Published on 15 Apr 2026 - 0:37

118

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How can I show the following trigonometric function

Published on 12 Apr 2026 - 4:09

650

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When does $f(X) = g(X+1)-g(X)$ where $f, g \in \mathbb{C}(X)$?

Published on 19 Apr 2026 - 0:18

725

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What can be said about the level set of the real part of an analytic function?

Published on 13 Apr 2026 - 8:21

436

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Image of the set under $f(z)=\frac{z-i}{z-1}$

Published on 15 Apr 2026 - 3:07

207

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Differential of complex-valued 1-form

Published on 17 Apr 2026 - 4:29

143

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Solve $\int_{|z|=3}\frac{\mathrm{e}^{\frac1{1-z}}}z\,\mathrm{d}z$

Published on 16 Apr 2026 - 7:17

457

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Verification of proof if $C$ is a positively oriented circle and $z_{0}$ lies outside $C$

Published on 13 Apr 2026 - 3:20

673

Views

Prove that $\arcsin(z)=\frac{\pi}{2}+i\log(z+i\sqrt{1-z^2})$

Published on 15 Apr 2026 - 23:26

1.1k

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Let C be the unit square with diagonal corners at $−1 − i$ and $1 + i$. Evaluate $\oint_C\frac{1}{2z+1}\mathrm{d}z$

Published on 14 Apr 2026 - 2:43

1.2k

Views

45 and 90-degree Phase shift

Published on 13 Apr 2026 - 11:24

103

Views

Evaluate integral using residues at $\infty$

Published on 13 Apr 2026 - 22:09

523

Views

Square root of operators over $\mathbb{C}^n$

Published on 13 Apr 2026 - 5:50

136

Views

Optimal bound on a problem similar to Schwarz lemma

Published on 09 Apr 2026 - 3:42

133

Views

$\log(z)$ for $|z| < 1$

Published on 15 Apr 2026 - 8:56

List Question

If $U$ is simply connected and $u: U\to\Bbb R$ is harmonic then it have a conjugate in $U$

How can I show the following trigonometric function

When does $f(X) = g(X+1)-g(X)$ where $f, g \in \mathbb{C}(X)$?

What can be said about the level set of the real part of an analytic function?

Image of the set under $f(z)=\frac{z-i}{z-1}$

Differential of complex-valued 1-form

Solve $\int_{|z|=3}\frac{\mathrm{e}^{\frac1{1-z}}}z\,\mathrm{d}z$

Verification of proof if $C$ is a positively oriented circle and $z_{0}$ lies outside $C$

Prove that $\arcsin(z)=\frac{\pi}{2}+i\log(z+i\sqrt{1-z^2})$

Let C be the unit square with diagonal corners at $−1 − i$ and $1 + i$. Evaluate $\oint_C\frac{1}{2z+1}\mathrm{d}z$

45 and 90-degree Phase shift

Evaluate integral using residues at $\infty$

Square root of operators over $\mathbb{C}^n$

Optimal bound on a problem similar to Schwarz lemma

$\log(z)$ for $|z| < 1$

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