Question

Prove that $\frac{1}{f'(a)} = \frac{1}{2\pi i} \int_C \frac{1}{f(z)-f(a)} dz$

score 554 · Answer 1 · 2026-04-15 23:06:23

554

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Prove that $\frac{1}{f'(a)} = \frac{1}{2\pi i} \int_C \frac{1}{f(z)-f(a)} dz$

Published on 15 Apr 2026 - 23:06

score 199 · Answer 2 · 2026-04-11 17:59:22

199

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closed continuous path in $\mathbb{C}$ homotopic to polygon

Published on 11 Apr 2026 - 17:59

score 347 · Answer 3 · 2026-04-13 17:00:16

347

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Prove that the principal logarithm ($Log$) is a bijection between $\mathbb{C}-[0,\infty)$ and $\Omega=\{z \in \mathbb{C} | -\pi < Im(z) <\pi\}$

Published on 13 Apr 2026 - 17:00

score 59 · Answer 4 · 2026-04-15 07:33:09

59

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Find $\oint\limits_{|z-\frac{1}{3}|=3} z \text{Im}(z)\text{d}z$

Published on 15 Apr 2026 - 7:33

score 298 · Answer 5 · 2026-03-25 01:37:46

298

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How the inverse of an holomorphic function becomes multivalued due to its critical points?

Published on 25 Mar 2026 - 1:37

score 646 · Answer 6 · 2026-04-09 02:23:24

646

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Do we have a conformal mapping from the regular pentagon to the disk?

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score 82 · Answer 7 · 2026-04-10 05:26:07

82

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How can I find the other solutions of $\sqrt{i}$?

Published on 10 Apr 2026 - 5:26

score 298 · Answer 8 · 2026-04-16 07:16:25

298

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Evaluating $\int\limits_0^\infty{\frac{1}{1+x^2+x^\alpha}dx}$

Published on 16 Apr 2026 - 7:16

score 2k · Answer 9 · 2026-04-16 08:20:08

2k

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Expand in Laurent series $f(z) = \frac{(z-2)}{ z^2 + 3z - 4}$ , by powers of $z$

Published on 16 Apr 2026 - 8:20

score 616 · Answer 10 · 2026-04-16 10:29:23

616

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How to prove $\log(\exp(z))\neq z$ if $z\in \mathbb{C}$

Published on 16 Apr 2026 - 10:29

score 158 · Answer 11 · 2026-04-19 01:37:17

158

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Integral on semicircular arc of a function with a simple pole at $z=0$

Published on 19 Apr 2026 - 1:37

score 770 · Answer 12 · 2026-04-14 20:46:56

770

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A counterexample of the converse of the theorem of sequence and its function

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score 52 · Answer 13 · 2026-04-11 22:22:59

52

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score 155 · Answer 14 · 2026-04-09 18:29:03

155

Views

What are the 'areas' of complex analysis

Published on 09 Apr 2026 - 18:29

score 66 · Answer 15 · 2026-04-16 04:54:08

66

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what is the radius of convergence of $\sum_{k=0}^\infty \frac{(−1)^k}{k!(n+k)!}\frac{z^{n+2k}}{2^{n+2k}}$

Published on 16 Apr 2026 - 4:54

List Question

Prove that $\frac{1}{f'(a)} = \frac{1}{2\pi i} \int_C \frac{1}{f(z)-f(a)} dz$

closed continuous path in $\mathbb{C}$ homotopic to polygon

Prove that the principal logarithm ($Log$) is a bijection between $\mathbb{C}-[0,\infty)$ and $\Omega=\{z \in \mathbb{C} | -\pi < Im(z) <\pi\}$

Find $\oint\limits_{|z-\frac{1}{3}|=3} z \text{Im}(z)\text{d}z$

How the inverse of an holomorphic function becomes multivalued due to its critical points?

Do we have a conformal mapping from the regular pentagon to the disk?

How can I find the other solutions of $\sqrt{i}$?

Evaluating $\int\limits_0^\infty{\frac{1}{1+x^2+x^\alpha}dx}$

Expand in Laurent series $f(z) = \frac{(z-2)}{ z^2 + 3z - 4}$ , by powers of $z$

How to prove $\log(\exp(z))\neq z$ if $z\in \mathbb{C}$

Integral on semicircular arc of a function with a simple pole at $z=0$

A counterexample of the converse of the theorem of sequence and its function

About the continuity of a partial derivative

What are the 'areas' of complex analysis

what is the radius of convergence of $\sum_{k=0}^\infty \frac{(−1)^k}{k!(n+k)!}\frac{z^{n+2k}}{2^{n+2k}}$

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