query: Principal value of the argument of z
positive_passages.docid: 17620
positive_passages.text: Why the principal value of complex number argument is taken within $(-\pi,\pi]?$
negative_passages.docid: 28218
negative_passages.text: Elementary proof for $\sqrt[3]{xyz} \leq \dfrac{x+y+z}{3}$
negative_passages.docid: 108921
negative_passages.text: By substituting $z = h(t)$ show that $\delta(h(t))=\sum\limits_{i}\frac{\delta(t−t_i)}{\mid h^{\prime}(t_i)\mid}$
negative_passages.docid: 41069
negative_passages.text: Justifying $\,\Bbb{Z}[i]/\langle 2\rangle\cong \Bbb{Z}[X]/\langle X^2+1,2\rangle\cong \Bbb{F}_2[X]/\langle X^2+1\rangle$
negative_passages.docid: 149783
negative_passages.text: $\mathbb Z\times\mathbb Z$ is principal but is not a PID
negative_passages.docid: 136855
negative_passages.text: Proof that $\mathbb{Z}\left[\frac{1 + \sqrt{-19}}{2}\right]$ is a PID
negative_passages.docid: 1043
negative_passages.text: Image of $L=\{z\in\Bbb C \mid a\operatorname{Re}(z)+b\operatorname{Im}(z)+c=0; a^2+b^2\neq0; a,b,c\in \Bbb R \}$ under the function $e^z$
negative_passages.docid: 32589
negative_passages.text: Prove or disprove that Arg(zw)=Arg(z)+Arg(w)
negative_passages.docid: 25618
negative_passages.text: $x,y,z$ independent and uniform random on $[0,1]$, $P(x \geq  yz)$?
negative_passages.docid: 148178
negative_passages.text: What points in the complex plane satisfy $|z|=arg(z)$.
negative_passages.docid: 28145
negative_passages.text: What is $\Gamma(z) \Gamma(\bar {z})$?
negative_passages.docid: 145752
negative_passages.text: Aut $\mathbb Z_p\simeq \mathbb Z_{p-1}$
negative_passages.docid: 145879
negative_passages.text: $R$ is PID, so $R/I$ is PID, and application on $\mathbb{Z}$ and $\mathbb{N}$
negative_passages.docid: 90273
negative_passages.text: Primitive roots of the unity in $\mathbb C$
negative_passages.docid: 17751
negative_passages.text: Find the greatest value of $\arg z$ achieved on a circle in $\mathbb{C}$
negative_passages.docid: 33300
negative_passages.text: Showing order of $Z (G) =1$ or $pq$
negative_passages.docid: 113612
negative_passages.text: Why does $P(\theta_1\mid D, \theta_2) \propto P(D \mid \theta_1, \theta_2)P(\theta_1)$ hold?