Question

How to prove that $\frac{1}{2} \left( 1 - \sqrt{3} \pm i \sqrt{2} \sqrt[4]{3} \right)$ is not a root of unity?

score 140 · Answer 1 · 2021-03-11 15:18:03

140

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How to prove that $\frac{1}{2} \left( 1 - \sqrt{3} \pm i \sqrt{2} \sqrt[4]{3} \right)$ is not a root of unity?

Published on 11 Mar 2021 - 15:18

score 236 · Answer 2 · 2021-03-24 09:20:18

236

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minimal polynomial of $7^{th}$ root of unity

Published on 24 Mar 2021 - 9:20

score 119 · Answer 3 · 2026-03-30 02:11:25

119

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Alternating series of powers of Cosine-squared

Published on 30 Mar 2026 - 2:11

score 86 · Answer 4 · 2021-03-25 19:38:02

86

Views

Is $1^\frac{1}{3}$ ambiguous?

Published on 25 Mar 2021 - 19:38

score 414 · Answer 5 · 2021-03-27 13:58:32

414

Views

If $\omega$ is nth root of unity evaluate $(1-\omega)(1-\omega^2)...(1-\omega^{n-1})$

Published on 27 Mar 2021 - 13:58

score 44 · Answer 6 · 2021-03-30 23:41:45

44

Views

Prove $\{x\in R | x^n-1=0\}=\{1,\omega,\dots,\omega^{n-1}\}.$ $R$ is any commutative ring with $1$ (a famous algorithm book by Aho, Hopcroft, Ullman)

Published on 30 Mar 2021 - 23:41

score 381 · Answer 7 · 2021-03-31 08:58:14

381

Views

Eigenvalues and roots of unity for integer coefficients matrix

Published on 31 Mar 2021 - 8:58

score 78 · Answer 8 · 2021-04-01 02:28:56

78

Views

Prove $\psi^n=-1$ ("The Design and Analysis of Computer Algorithms" by Aho, Hopcroft, Ullman)

Published on 01 Apr 2021 - 2:28

score 252 · Answer 9 · 2021-04-01 21:48:57

252

Views

Advanced complex numbers/roots of unity

Published on 01 Apr 2021 - 21:48

score 118 · Answer 10 · 2021-04-07 19:28:09

118

Views

Which real numbers are contained in $\mathbb{Q}(\cos40+i\sin40)$?

Published on 07 Apr 2021 - 19:28

score 134 · Answer 11 · 2026-03-27 14:39:49

134

Views

Let $G$ be the multiplicative group of all complex $2^n$th roots of unity, $n=0, 1, 2,\dots$. Prove that [. . .] every subgroup is marginal.

Published on 27 Mar 2026 - 14:39

score 156 · Answer 12 · 2021-04-15 02:16:00

156

Views

Sum of roots of unity equal to a fix number

Published on 15 Apr 2021 - 2:16

score 99 · Answer 13 · 2026-02-23 05:47:43

99

Views

Show that the group of all complex $2^n$th roots of unity, $n=0,1,2,...$, has a fully-invariant subgroup which is not verbal

Published on 23 Feb 2026 - 5:47

score 99 · Answer 14 · 2026-03-27 15:36:12

99

Views

Complex roots of quartic equation during solution of $z^5=1$

Published on 27 Mar 2026 - 15:36

score 58 · Answer 15 · 2021-04-23 21:25:24

58

Views

Existence of onto Homomorphism

Published on 23 Apr 2021 - 21:25

List Question

How to prove that $\frac{1}{2} \left( 1 - \sqrt{3} \pm i \sqrt{2} \sqrt[4]{3} \right)$ is not a root of unity?

minimal polynomial of $7^{th}$ root of unity

Alternating series of powers of Cosine-squared

Is $1^\frac{1}{3}$ ambiguous?

If $\omega$ is nth root of unity evaluate $(1-\omega)(1-\omega^2)...(1-\omega^{n-1})$

Prove $\{x\in R | x^n-1=0\}=\{1,\omega,\dots,\omega^{n-1}\}.$ $R$ is any commutative ring with $1$ (a famous algorithm book by Aho, Hopcroft, Ullman)

Eigenvalues and roots of unity for integer coefficients matrix

Prove $\psi^n=-1$ ("The Design and Analysis of Computer Algorithms" by Aho, Hopcroft, Ullman)

Advanced complex numbers/roots of unity

Which real numbers are contained in $\mathbb{Q}(\cos40+i\sin40)$?

Let $G$ be the multiplicative group of all complex $2^n$th roots of unity, $n=0, 1, 2,\dots$. Prove that [. . .] every subgroup is marginal.

Sum of roots of unity equal to a fix number

Show that the group of all complex $2^n$th roots of unity, $n=0,1,2,...$, has a fully-invariant subgroup which is not verbal

Complex roots of quartic equation during solution of $z^5=1$

Existence of onto Homomorphism

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