query: A complex root of unity and "dense" property of the its orbit on the unit circle
positive_passages.docid: 30568
positive_passages.text: Let $q \in \mathbb C$, $\|q\|=1$ and $q^n \neq 1, \forall n \in \mathbb N$. Show that $\{q^n: n \in \mathbb N\}$ is dense in $S^1$
negative_passages.docid: 103552
negative_passages.text: The minimal polynomial of a primitive $p^{m}$-th root of unity over $\mathbb{Q}_p$
negative_passages.docid: 149319
negative_passages.text: Möbius transformations and concentric circles
negative_passages.docid: 140851
negative_passages.text: Precalculus unit circle with imaginary axis.
negative_passages.docid: 145509
negative_passages.text: Prove the roots of $p(z)+z^n\bar{p}(\frac{1}{z})$ lie on the unit circle
negative_passages.docid: 109760
negative_passages.text: Showing that the product of all $n$th Roots of Unity is $(-1)^{n+1}$
negative_passages.docid: 58448
negative_passages.text: Complex:Schwarz lemma
negative_passages.docid: 129943
negative_passages.text: Torsion on $\pi_1(X)$, $X$ connected and open in $\mathbb{R}^n$
negative_passages.docid: 103328
negative_passages.text: Rational Roots of Riemann's $\zeta$ Function
negative_passages.docid: 42165
negative_passages.text: Complex numbers and Roots of unity
negative_passages.docid: 84374
negative_passages.text: Rational function with absolute value $1$ on unit circle
negative_passages.docid: 20305
negative_passages.text: Complex roots of $z^3 + \bar{z} = 0$
negative_passages.docid: 125474
negative_passages.text: Exercise 16 from chapter 3 of Stein & Shakarchi's complex analysis
negative_passages.docid: 111898
negative_passages.text: Is $\{ (e^{2\pi i a n},e^{2\pi i b n }) : n \in \mathbb{Z} \}$ dense in the torus, where $a,b$ irrationals such that $a/b$ irrational?
negative_passages.docid: 157200
negative_passages.text: Roots of a equation on a complex plane
negative_passages.docid: 82458
negative_passages.text: Homeomorphism between the unit disc and the unit square
negative_passages.docid: 136635
negative_passages.text: Proving that the Fourier Basis is complete for C(R/$2*\pi$ , C) with $L^2$ norm