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On multiplicative and additive properties of cyclotomic polynomials

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#polynomials #roots-of-unity #primitive-roots #cyclotomic-polynomials #big-picture
812
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Roots of $z^3 + 3iz^2 + 3z + i = 0$?

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#complex-numbers #cubics #roots-of-unity
77
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Compute the determinant.

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#determinant #roots-of-unity
128
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Polygon discriminant sequence

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#abstract-algebra #sequences-and-series #algebraic-geometry #roots-of-unity
244
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Is $\sqrt[6]{3} \in \mathbb{Q}(\sqrt[8]{21})$ and/or $\sqrt[4]{5} \in \mathbb{Q}(e^{\frac{2 \pi i}{25}})$?

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#abstract-algebra #galois-theory #extension-field #roots-of-unity
156
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How to prove the following identity using complex numbers?

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#trigonometry #complex-numbers #products #roots-of-unity
179
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Why does $\sqrt[4]{-2}=\frac{1+i}{\sqrt[4]{2}}$?

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#complex-numbers #roots #radicals #roots-of-unity
369
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Square root of a root of unity.

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#number-theory #roots-of-unity
134
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Rational Trig Solutions for $n\ge 3$

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#trigonometry #rational-numbers #roots-of-unity #golden-ratio
112
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Solving simultaneous equations using de Moivre's Theorem and Roots of Unity

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#complex-numbers #systems-of-equations #roots-of-unity
63
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Integration by substitution and root of unity

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#integration #substitution #roots-of-unity
324
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Sum of $1/(1 - x)$ over roots of unity

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#abstract-algebra #complex-analysis #elementary-number-theory #roots-of-unity
117
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Sum involving powers of roots of unity

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#combinatorics #number-theory #roots-of-unity
255
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nth root of unity problem for homework

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#roots-of-unity
85
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Can this polynomial be solved over the roots of unity for $n\ge 3$?

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#polynomials #roots-of-unity

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