Question

If $α,β,γ$ belong to ${1,w,w^2}$ then how is number of triplets satisfying $|(aα+bβ+cγ)/(aβ+bγ+cα)| = 1$ equal to $9$?

score 634 · Answer 1 · 2026-03-26 01:29:08

634

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If $α,β,γ$ belong to ${1,w,w^2}$ then how is number of triplets satisfying $|(aα+bβ+cγ)/(aβ+bγ+cα)| = 1$ equal to $9$?

Published on 26 Mar 2026 - 1:29

score 56 · Answer 2 · 2026-03-24 12:55:01

56

Views

Determine all limits of subsequences of $|\lambda \alpha^n +\mu \bar{\alpha}^n|$ (assume $|\alpha|>1$)

Published on 24 Mar 2026 - 12:55

score 59 · Answer 3 · 2026-03-25 23:35:13

59

Views

Geometry Complex Numbers Convexity

Published on 25 Mar 2026 - 23:35

score 99 · Answer 4 · 2018-05-07 13:00:16

99

Views

The number of imaginary roots of $\sum_{n=1}^{100} \frac {n^2}{x-x_{n} }= 101$, where each $x_n$ is real

Published on 07 May 2018 - 13:00

score 53 · Answer 5 · 2026-03-25 12:55:31

53

Views

Homomorphisms from nonabelian simple groups into $\mathbb{C}^\times$

Published on 25 Mar 2026 - 12:55

score 601 · Answer 6 · 2018-05-07 15:45:05

601

Views

How do I show that a complex number $z$ is a root of $z^6-1$?

Published on 07 May 2018 - 15:45

score 61 · Answer 7 · 2018-05-07 15:47:44

61

Views

Bases de una matriz

Published on 07 May 2018 - 15:47

score 64 · Answer 8 · 2018-05-07 18:13:31

64

Views

How do I add the complex numbers $z^4$ and $z$?

Published on 07 May 2018 - 18:13

score 1.9k · Answer 9 · 2026-03-25 19:07:06

1.9k

Views

If $z_1+z_2+z_3=0$ and $|z_1|=|z_2|=|z_3|=1$, then $z_1,z_2,z_3$ are the vertices of an equilateral triangle.

Published on 25 Mar 2026 - 19:07

score 67 · Answer 10 · 2026-03-25 14:18:43

67

Views

proving $|\lambda_1|<1<|\lambda_2|$.

Published on 25 Mar 2026 - 14:18

score 76 · Answer 11 · 2018-05-08 13:14:57

76

Views

Tell whether module of root of such polynomial is smaller than 1

Published on 08 May 2018 - 13:14

score 62 · Answer 12 · 2018-05-08 13:44:38

62

Views

Prove $e^{|z|}-1\geq|e^z-1|$

Published on 08 May 2018 - 13:44

score 51 · Answer 13 · 2018-05-08 17:04:17

51

Views

Complex numbers finding roots

Published on 08 May 2018 - 17:04

score 623 · Answer 14 · 2018-05-08 21:13:02

623

Views

Can we always use Euler's formula for complex numbers?

Published on 08 May 2018 - 21:13

score 116 · Answer 15 · 2018-05-08 21:26:08

116

Views

Can we revert law of cosines into its original complex identity?

Published on 08 May 2018 - 21:26

List Question

If $α,β,γ$ belong to ${1,w,w^2}$ then how is number of triplets satisfying $|(aα+bβ+cγ)/(aβ+bγ+cα)| = 1$ equal to $9$?

Determine all limits of subsequences of $|\lambda \alpha^n +\mu \bar{\alpha}^n|$ (assume $|\alpha|>1$)

Geometry Complex Numbers Convexity

The number of imaginary roots of $\sum_{n=1}^{100} \frac {n^2}{x-x_{n} }= 101$, where each $x_n$ is real

Homomorphisms from nonabelian simple groups into $\mathbb{C}^\times$

How do I show that a complex number $z$ is a root of $z^6-1$?

Bases de una matriz

How do I add the complex numbers $z^4$ and $z$?

If $z_1+z_2+z_3=0$ and $|z_1|=|z_2|=|z_3|=1$, then $z_1,z_2,z_3$ are the vertices of an equilateral triangle.

proving $|\lambda_1|<1<|\lambda_2|$.

Tell whether module of root of such polynomial is smaller than 1

Prove $e^{|z|}-1\geq|e^z-1|$

Complex numbers finding roots

Can we always use Euler's formula for complex numbers?

Can we revert law of cosines into its original complex identity?

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