List questions from roots-of-unity

Published on 25 Mar 2026 - 16:45

112

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How do unity roots relate to the summation?

Published on 17 Mar 2023 - 2:43

62

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Show that $\sum_{j=0}^{n-1} {|{z_1} + {\omega}^j{z_2}|}^2 = n(|{z_1}|^2 + |{z_2}|^2)$

Published on 18 Mar 2023 - 14:17

70

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Integer polynomials such that $f(z) = 0, |z| = 1$

Published on 20 Mar 2023 - 12:29

139

Views

Norm of a root of unity $\zeta$ is $1$ only if $\zeta=1$?

Published on 26 Mar 2026 - 3:01

39

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Is every complex root of an integer polynomial a product of an algebraic real number and a root of unity?

Published on 23 Feb 2026 - 8:34

160

Views

Product of differences of roots of unity

Published on 01 Apr 2023 - 3:03

161

Views

Prove that $yx = qxy$ implies $(x + y)^d = x^d + y^d.$

Published on 06 Apr 2023 - 23:39

72

Views

Why is my equation not true on all elements?

Published on 10 Apr 2023 - 11:31

252

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Why does there seem to be a relation between the fifth roots of $32$ and $\varphi$ (the golden ratio)?

Published on 26 Mar 2026 - 6:34

30

Views

What is known about the minimal absolute value in $\mathbb{Z}[\zeta_n]\setminus\{0\}$?

Published on 23 Feb 2026 - 13:03

103

Views

Prove all Lie group homomorphisms of the circle have certain form

Published on 23 Apr 2023 - 8:24

959

Views

Significance of Roots of Unity

Published on 28 Apr 2023 - 3:32

120

Views

Double factorial & roots of unity filter

Published on 01 May 2023 - 3:34

182

Views

Any unit in $\Bbb Z[\zeta_p]$ can be decomposed into a power of $\zeta_p$ and a real unit in $\Bbb Z[\zeta_p]$

Published on 25 Mar 2026 - 16:20

List Question

Multiplicative complex function has mean value

How do unity roots relate to the summation?

Show that $\sum_{j=0}^{n-1} {|{z_1} + {\omega}^j{z_2}|}^2 = n(|{z_1}|^2 + |{z_2}|^2)$

Integer polynomials such that $f(z) = 0, |z| = 1$

Norm of a root of unity $\zeta$ is $1$ only if $\zeta=1$?

Is every complex root of an integer polynomial a product of an algebraic real number and a root of unity?

Product of differences of roots of unity

Prove that $yx = qxy$ implies $(x + y)^d = x^d + y^d.$

Why is my equation not true on all elements?

Why does there seem to be a relation between the fifth roots of $32$ and $\varphi$ (the golden ratio)?

What is known about the minimal absolute value in $\mathbb{Z}[\zeta_n]\setminus\{0\}$?

Prove all Lie group homomorphisms of the circle have certain form

Significance of Roots of Unity

Double factorial & roots of unity filter

Any unit in $\Bbb Z[\zeta_p]$ can be decomposed into a power of $\zeta_p$ and a real unit in $\Bbb Z[\zeta_p]$

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