Sum of the roots of unity, $z_{1}^p+...+z_{n}^p$
31977
How to prove sum of powers property of roots of unity?
111199
Does there exist a formula for product of the primitive $ n $th roots of unity.
120215
Sum of elements of a finite field
44928
Show $\sum_n \frac{z^{2^n}}{1-z^{2^{n+1}}} = \frac{z}{1-z}$
89758
Is there a formula for $(1+i)^n+(1-i)^n$?
154544
Prove that $ \sum_{n=0}^\infty \frac{z^{2^n}}{1-z^{2^{n+1}}}=\frac{z}{1-z} $
118105
What is the radius of convergence of $\sum z^{n!}$?
54374
Alternating Series Using Other Roots of Unity
114414
Sum of $\sum_{k=1}^n\sin{k\theta}$
88656
For $p$ prime, show that $\Phi_{p^n}(x) = 1 + x^{p^{n-1}} + x^{2p^{n-2}} + \dots +x^{(p-1)^{p^n-1}}$
90273
Primitive roots of the unity in $\mathbb C$
92440
Let $n \in \mathbb{Z}^+$, prove the identity $ \sum_{k=1}^{n-1} \binom {n} {k} \frac{kn^{n-k}}{k+1}=\frac{n(n^{n}-1)}{n+1}$
63965
How can I compute the sum of $ {m\over\gcd(m,n)}$?
102942
Compute the sum $\sum_{k=1}^{\infty}k^mz^k$ where $|z|<1$
37771
Sum of a power series $n x^n$
68458
Roots of unity and large expression
69618
What is the sum of non-real roots of the polynomial equation?