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Sum of roots of unity an algebraic integer proof

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#number-theory #algebraic-number-theory #galois-theory #roots-of-unity #cyclotomic-polynomials
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Find $z^{10}+\frac{1}{z^{10}}$ given $z^2+z+1=0$

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#complex-numbers #roots-of-unity
273
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When is a sum of consecutive roots of unity an integer

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#number-theory #roots-of-unity #cyclotomic-polynomials
619
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$p$-adic $n$-th root of unity and $\exp(2\pi i /n)$

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#roots-of-unity
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How to solve $z^6+i=0$

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#polynomials #complex-numbers #roots #roots-of-unity
143
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Question Primitive Roots of Unity

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#roots-of-unity
225
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What is the value of $\sum_{m=1}^{19} \frac{1}{\zeta^{3m}+\zeta^{2m}+\zeta^{m}+1}$ with $\zeta=e^{2\pi i/19}$?

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#complex-analysis #summation #roots-of-unity
201
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Product of roots of unity

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#modular-arithmetic #divisibility #products #roots-of-unity
157
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summation and product of sin and cos

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#complex-numbers #summation #products #roots-of-unity
150
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If $w = e^{2i\pi/5} $, then $1 + w + w^{2} + w^{3} + 5w^{4} + 4w^{5} + 4w^{6} + 4w^{7} + 4w^{8} + 5w^{9}$=?

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#complex-numbers #roots-of-unity
864
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How can I find fifth root of unity?

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#proof-verification #roots-of-unity #trigonometric-series
3.5k
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Eigenvalues and roots of unity

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#linear-algebra #complex-numbers #eigenvalues-eigenvectors #roots-of-unity
54
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Are conditions equaivalent that they are roots of unity?

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#complex-numbers #roots-of-unity
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Show that complex numbers are vertices of equilateral triangle

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#trigonometry #complex-numbers #roots-of-unity
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Norm of an element in cyclotomic extension (Exercises VI.19 Lang's Algebra)

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#abstract-algebra #field-theory #galois-theory #roots-of-unity #cyclotomic-polynomials

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