Question

Visual Intuitive for Residue Theorem

score 275 · Answer 1 · 2026-04-10 16:51:13

275

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Visual Intuitive for Residue Theorem

Published on 10 Apr 2026 - 16:51

score 82 · Answer 2 · 2026-04-15 19:45:44

82

Views

Find $a, b \in \mathbb{R}$ if $a+ia$ is a root of the equation $z^2+4z+b=0$.

Published on 15 Apr 2026 - 19:45

score 29 · Answer 3 · 2026-04-14 00:18:52

29

Views

All possible values of the integral

Published on 14 Apr 2026 - 0:18

score 49 · Answer 4 · 2026-04-16 01:07:45

49

Views

$(a+bi)$ of $\frac{3+4i}{5+6i}$ and $i^{2006}$ and $\frac{1}{\frac{1}{1+i}-1}$

Published on 16 Apr 2026 - 1:07

score 185 · Answer 5 · 2026-04-15 22:35:08

185

Views

Prove that $\frac{1}{\sin z} = \frac{1}{z} + \sum_{n=1}^{\infty} \frac{(-1)^n 2z}{z^2 - \pi^2 n^2}$

Published on 15 Apr 2026 - 22:35

score 51 · Answer 6 · 2026-04-14 09:44:10

51

Views

Complex numbers $a \ne 0$ and $b \ne 0$ such that for all positive integer $n$ the equality $a^{2017^n}+b^{2017^n}=1$ holds

Published on 14 Apr 2026 - 9:44

score 37 · Answer 7 · 2026-04-15 19:07:40

37

Views

For rational functions, do we always know the order of the pole?

Published on 15 Apr 2026 - 19:07

score 2.4k · Answer 8 · 2026-04-16 05:10:19

2.4k

Views

show that the root of (x+1)^7 = (x-1)^7 are given by -+cotrπ/7, r=1,2,3

Published on 16 Apr 2026 - 5:10

score 68 · Answer 9 · 2026-04-16 04:05:30

68

Views

Sequence of holomorphic functions that converge compactly in Upper Half Plane $\operatorname{Im}(x)>0$ but not in $\mathbb{C}$

Published on 16 Apr 2026 - 4:05

score 86 · Answer 10 · 2026-04-16 07:27:57

86

Views

Find all the actual $ x $ values that satisfy the following inequality

Published on 16 Apr 2026 - 7:27

score 134 · Answer 11 · 2026-04-12 07:46:49

134

Views

A closed form for $\Re\sum_{k=1}^\infty\dfrac{i^{\sigma_0(k)}}k$

Published on 12 Apr 2026 - 7:46

score 359 · Answer 12 · 2026-04-16 05:00:44

359

Views

Why doesn't $1/i$ equal $i$?

Published on 16 Apr 2026 - 5:00

score 28 · Answer 13 · 2026-04-16 03:39:35

28

Views

Find the minimum value of $|z_1−z_2|$ of $e^{ia}z^2-(i+3e ^{3ia}) z+3ie^{2ia}=0$

Published on 16 Apr 2026 - 3:39

score 50 · Answer 14 · 2026-04-15 17:17:13

50

Views

Is $\lim_{z\rightarrow 1}\frac{z_0}{\log(\frac{1}{z-1})}=0$?

Published on 15 Apr 2026 - 17:17

score 4.5k · Answer 15 · 2026-04-11 14:27:52

4.5k

Views

How to solve complex number equation: $z^5=\bar z$?

Published on 11 Apr 2026 - 14:27

List Question

Visual Intuitive for Residue Theorem

Find $a, b \in \mathbb{R}$ if $a+ia$ is a root of the equation $z^2+4z+b=0$.

All possible values of the integral

$(a+bi)$ of $\frac{3+4i}{5+6i}$ and $i^{2006}$ and $\frac{1}{\frac{1}{1+i}-1}$

Prove that $\frac{1}{\sin z} = \frac{1}{z} + \sum_{n=1}^{\infty} \frac{(-1)^n 2z}{z^2 - \pi^2 n^2}$

Complex numbers $a \ne 0$ and $b \ne 0$ such that for all positive integer $n$ the equality $a^{2017^n}+b^{2017^n}=1$ holds

For rational functions, do we always know the order of the pole?

show that the root of (x+1)^7 = (x-1)^7 are given by -+cotrπ/7, r=1,2,3

Sequence of holomorphic functions that converge compactly in Upper Half Plane $\operatorname{Im}(x)>0$ but not in $\mathbb{C}$

Find all the actual $ x $ values that satisfy the following inequality

A closed form for $\Re\sum_{k=1}^\infty\dfrac{i^{\sigma_0(k)}}k$

Why doesn't $1/i$ equal $i$?

Find the minimum value of $|z_1−z_2|$ of $e^{ia}z^2-(i+3e ^{3ia}) z+3ie^{2ia}=0$

Is $\lim_{z\rightarrow 1}\frac{z_0}{\log(\frac{1}{z-1})}=0$?

How to solve complex number equation: $z^5=\bar z$?

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