Question

Trigonometric values in the complex plane

score 56 · Answer 1 · 2018-03-26 23:39:36

56

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Trigonometric values in the complex plane

Published on 26 Mar 2018 - 23:39

score 76 · Answer 2 · 2018-03-27 10:59:55

76

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Proving that $ \mid z+1\mid^{2}=2\mid z\mid^{2} \Leftrightarrow \mid z-1\mid^{2}=2 $

Published on 27 Mar 2018 - 10:59

score 732 · Answer 3 · 2026-03-25 12:51:03

732

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For $z_1, z_2 \in \mathbb C$ prove that $|z_1+z_2|^2+|z_1-z_2|^2=2(|z_1|^2+|z_2|^2)$, and interpret this result geometrically.

Published on 25 Mar 2026 - 12:51

score 59 · Answer 4 · 2018-03-27 18:16:14

59

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Complex equation simplification

Published on 27 Mar 2018 - 18:16

score 72 · Answer 5 · 2026-03-25 13:56:26

72

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Is there a way to simplify $\ln\left[ \Gamma\left( i x \right) \right] - \ln\left[ \Gamma\left( i y \right) \right]$?

Published on 25 Mar 2026 - 13:56

score 74 · Answer 6 · 2018-03-27 22:14:35

74

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Complex map exercise

Published on 27 Mar 2018 - 22:14

score 1.1k · Answer 7 · 2026-03-26 01:28:27

1.1k

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Analytic function at a point is analytic in a neighborhood

Published on 26 Mar 2026 - 1:28

score 47 · Answer 8 · 2026-03-25 22:26:49

47

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Show that if $z \in \Bbb C$ is such that $|z| < 1$, then $\sum_{n=0} ^{\infty} {a \choose n}z^n$ converges for any $a \in \Bbb C$.

Published on 25 Mar 2026 - 22:26

score 34 · Answer 9 · 2026-03-25 07:41:49

34

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Whe the conjugate operator in $\mathbb{C}$ is a automorphism?

Published on 25 Mar 2026 - 7:41

score 49 · Answer 10 · 2018-03-29 06:10:31

49

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Proving a series goes to infinity

Published on 29 Mar 2018 - 6:10

score 298 · Answer 11 · 2018-03-29 06:37:42

298

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Complex power series is arctan function

Published on 29 Mar 2018 - 6:37

score 198 · Answer 12 · 2026-03-25 19:51:39

198

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Showing $\mathbb{Z}[i]/(1+2i) \oplus\mathbb{Z}[i]/(6-i)\cong\mathbb{Z}[i]/(8+11i)$

Published on 25 Mar 2026 - 19:51

score 363 · Answer 13 · 2018-03-30 00:23:50

363

Views

Mobius transformations abelian

Published on 30 Mar 2018 - 0:23

score 75 · Answer 14 · 2018-03-30 09:37:50

75

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How to find a real $d \ne 0$ such that the equation $(2-3i) z^2 -(d-1)z + 4+ 3i = 0$ has a real root?

Published on 30 Mar 2018 - 9:37

score 7.7k · Answer 15 · 2026-03-26 20:07:54

7.7k

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Why $e^{i(π/3)} \ne -1$?

Published on 26 Mar 2026 - 20:07

List Question

Trigonometric values in the complex plane

Proving that $ \mid z+1\mid^{2}=2\mid z\mid^{2} \Leftrightarrow \mid z-1\mid^{2}=2 $

For $z_1, z_2 \in \mathbb C$ prove that $|z_1+z_2|^2+|z_1-z_2|^2=2(|z_1|^2+|z_2|^2)$, and interpret this result geometrically.

Complex equation simplification

Is there a way to simplify $\ln\left[ \Gamma\left( i x \right) \right] - \ln\left[ \Gamma\left( i y \right) \right]$?

Complex map exercise

Analytic function at a point is analytic in a neighborhood

Show that if $z \in \Bbb C$ is such that $|z| < 1$, then $\sum_{n=0} ^{\infty} {a \choose n}z^n$ converges for any $a \in \Bbb C$.

Whe the conjugate operator in $\mathbb{C}$ is a automorphism?

Proving a series goes to infinity

Complex power series is arctan function

Showing $\mathbb{Z}[i]/(1+2i) \oplus\mathbb{Z}[i]/(6-i)\cong\mathbb{Z}[i]/(8+11i)$

Mobius transformations abelian

How to find a real $d \ne 0$ such that the equation $(2-3i) z^2 -(d-1)z + 4+ 3i = 0$ has a real root?

Why $e^{i(π/3)} \ne -1$?

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