Question

Properties of complex logarithm

score 789 · Answer 1 · 2026-04-08 16:24:41

789

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Properties of complex logarithm

Published on 08 Apr 2026 - 16:24

score 244 · Answer 2 · 2019-09-01 00:39:22

244

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Evaluate $\sum\limits_{n=0}^{\infty} \frac{\cos(nx)}{2^n}$ where $\cos x = \frac15$

Published on 01 Sep 2019 - 0:39

score 80 · Answer 3 · 2019-09-01 03:50:18

80

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Consider the function $q(z)=\frac{1}{2}(z+z^{-1})$ for all $z\in\mathbb{C}\setminus{\{0}\}$, how many points do you have $q^{-1}(z)$?

Published on 01 Sep 2019 - 3:50

score 106 · Answer 4 · 2026-04-11 16:02:43

106

Views

$\operatorname{Tr}\det H$ of a $2\times 2$ block matrix $H$

Published on 11 Apr 2026 - 16:02

score 593 · Answer 5 · 2019-09-01 13:55:36

593

Views

How is the determinant related to the unit circle?

Published on 01 Sep 2019 - 13:55

score 101 · Answer 6 · 2019-09-01 19:21:50

101

Views

Since $\sqrt{-1}=i$ is wrong, what about $\sqrt{-4}$? Is it $2i$ or $\pm 2i$ or something else?

Published on 01 Sep 2019 - 19:21

score 353 · Answer 7 · 2026-04-11 16:56:23

353

Views

Does every complex $n$ by $n$ matrix have at least one eigenvector? Like is it possible for a complex square matrix to have zero eigenvectors?

Published on 11 Apr 2026 - 16:56

score 118 · Answer 8 · 2019-09-02 04:37:53

118

Views

Is $(-3)^\sqrt{2}$ a real number ? If it a complex number, then what is its $a+bi$ form?

Published on 02 Sep 2019 - 4:37

score 3.1k · Answer 9 · 2026-04-11 10:33:46

3.1k

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properties that real numbers hold but complex numbers does not

Published on 11 Apr 2026 - 10:33

score 163 · Answer 10 · 2026-04-09 11:02:41

163

Views

Prove that $\sum_{k=0}^{n-1} \frac{\cos(k\cos^{-1}x)}{x^k}=\frac {\sin(n\cos^{-1}x)}{x^{n-1}\sqrt[2]{1-x^2}} $

Published on 09 Apr 2026 - 11:02

score 36 · Answer 11 · 2026-04-11 19:54:26

36

Views

How to calculate $f^ {-1}(\mathbb{R})$ and $f(\partial\mathbb{E})$?

Published on 11 Apr 2026 - 19:54

score 938 · Answer 12 · 2019-09-02 21:33:41

938

Views

Finding smallest n satisfying $z^n$ is real and positive.

Published on 02 Sep 2019 - 21:33

score 197 · Answer 13 · 2019-09-03 06:25:39

197

Views

There is a holomorphic and bijective function of $\mathbb {D}$ in $\mathbb{D}\setminus(0,1]$?

Published on 03 Sep 2019 - 6:25

score 96 · Answer 14 · 2026-03-25 13:54:15

96

Views

How do I show this Mobius transformation maps the unit disk onto itself?

Published on 25 Mar 2026 - 13:54

score 103 · Answer 15 · 2019-09-03 13:10:49

103

Views

Show that $\mathbb{C}\setminus{\{0}\}$ is homogeneous with respect $Aut(\mathbb{C}\setminus{\{0}\}$)$

Published on 03 Sep 2019 - 13:10

List Question

Properties of complex logarithm

Evaluate $\sum\limits_{n=0}^{\infty} \frac{\cos(nx)}{2^n}$ where $\cos x = \frac15$

Consider the function $q(z)=\frac{1}{2}(z+z^{-1})$ for all $z\in\mathbb{C}\setminus{\{0}\}$, how many points do you have $q^{-1}(z)$?

$\operatorname{Tr}\det H$ of a $2\times 2$ block matrix $H$

How is the determinant related to the unit circle?

Since $\sqrt{-1}=i$ is wrong, what about $\sqrt{-4}$? Is it $2i$ or $\pm 2i$ or something else?

Does every complex $n$ by $n$ matrix have at least one eigenvector? Like is it possible for a complex square matrix to have zero eigenvectors?

Is $(-3)^\sqrt{2}$ a real number ? If it a complex number, then what is its $a+bi$ form?

properties that real numbers hold but complex numbers does not

Prove that $\sum_{k=0}^{n-1} \frac{\cos(k\cos^{-1}x)}{x^k}=\frac {\sin(n\cos^{-1}x)}{x^{n-1}\sqrt[2]{1-x^2}} $

How to calculate $f^ {-1}(\mathbb{R})$ and $f(\partial\mathbb{E})$?

Finding smallest n satisfying $z^n$ is real and positive.

There is a holomorphic and bijective function of $\mathbb {D}$ in $\mathbb{D}\setminus(0,1]$?

How do I show this Mobius transformation maps the unit disk onto itself?

Show that $\mathbb{C}\setminus{\{0}\}$ is homogeneous with respect $Aut(\mathbb{C}\setminus{\{0}\}$)$

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