query: $z^{3}$ is the conjugate of $z\in\mathbb{C}$
positive_passages.docid: 56341
positive_passages.text: Solving complex numbers equation $z^3 = \overline{z} $
negative_passages.docid: 93703
negative_passages.text: Groups of units of $\mathbb{Z}\left[\frac{1+\sqrt{-3}}{2}\right]$
negative_passages.docid: 90273
negative_passages.text: Primitive roots of the unity in $\mathbb C$
negative_passages.docid: 59995
negative_passages.text: Isomorphism between $\mathbb{C}^* $ under multiplication with $\mathbb{C}$ under addition.
negative_passages.docid: 121280
negative_passages.text: Proving that $a \mathbb{Z} \cap b\mathbb{Z} = \operatorname{lcm}(a,b)\mathbb Z$
negative_passages.docid: 6171
negative_passages.text: Isomorphism between $\Bbb{Z}[\sqrt{d}]$ and a quotient of $\Bbb{Z}[X].$
negative_passages.docid: 124438
negative_passages.text: Find $|(\mathbb{Z} \oplus \mathbb{Z}) / \langle(3,6)\rangle|$ and determine if its cyclic
negative_passages.docid: 132725
negative_passages.text: Is $\mathbb{Z}/\langle n\rangle$ cyclic and of order $n$?
negative_passages.docid: 48127
negative_passages.text: Are there infinitely many $A\in \mathbb{C}^{2 \times 2}$ satisfying $A^3 = A$?
negative_passages.docid: 87160
negative_passages.text: Prove $\mathbb{Z}_3[x]/(x^2+1)$ and $\mathbb{Z}_3[x]/(x^2+x-1)$ are isomorphic.
negative_passages.docid: 155275
negative_passages.text: If two real matrices are conjugated over $\mathbb{C}$, are they then also conjugated over $\mathbb{R}$?
negative_passages.docid: 135441
negative_passages.text: When is $\mathbb{Z}[\alpha]$ dense in $\mathbb{C}$?
negative_passages.docid: 123726
negative_passages.text: $2\times 2 $ matrices over $\mathbb{C}$ that satisfy $\mathrm A^3=\mathrm A$
negative_passages.docid: 98284
negative_passages.text: show $\Bbb Z_6 \cong \Bbb Z_3 \times \Bbb Z_2 $.
negative_passages.docid: 130104
negative_passages.text: Show $4x^2+6x+3$ is a unit in $\mathbb{Z}_8[x]$ (inverting unit + nilpotent)
negative_passages.docid: 37928
negative_passages.text: Isomorphism between $D_{2n}/Z(D_{2n})$ and $D_n$
negative_passages.docid: 92517
negative_passages.text: Easy way to show that $\mathbb{Z}[\sqrt[3]{2}]$ is the ring of integers of $\mathbb{Q}[\sqrt[3]{2}]$