query: I need toSolve this proof for complex numbers
positive_passages.docid: 23609
positive_passages.text: If a series converges, then the sequence of terms converges to $0$.
negative_passages.docid: 28218
negative_passages.text: Elementary proof for $\sqrt[3]{xyz} \leq \dfrac{x+y+z}{3}$
negative_passages.docid: 16774
negative_passages.text: If $x,y,z\in\mathbb R\setminus \{1\}$ and $xyz=1$, prove that $\frac{x^2}{(x-1)^2}+\frac{y^2}{(y-1)^2}+\frac{z^2}{(z-1)^2}\ge 1$.
negative_passages.docid: 56697
negative_passages.text: How to show that the given equation has at least one complex root ,a s.t |a|>12
negative_passages.docid: 117680
negative_passages.text: Prove that $|e^{i\theta_1}-e^{i\theta_2}| \leq |\theta_1 - \theta_2|$
negative_passages.docid: 92595
negative_passages.text: A problem regarding the in-equality of complex numbers .
negative_passages.docid: 136721
negative_passages.text: Absolute value of a complex number proof
negative_passages.docid: 111094
negative_passages.text: Help with proving that $\pi$ is irrational
negative_passages.docid: 114734
negative_passages.text: Prove that $\frac{1}{2\pi i}\int_\mathcal{C} |1+z+z^2+\cdots+z^{2n}|^2~dz =2n$ where $\mathcal{C}$ is the unit circle
negative_passages.docid: 15237
negative_passages.text: Prove an inequality using complex analysis
negative_passages.docid: 18285
negative_passages.text: Prove that $\prod_{k=1}^{n-1}\sin\frac{k \pi}{n} = \frac{n}{2^{n-1}}$
negative_passages.docid: 110826
negative_passages.text: prove that : $ i = \sqrt {-1}\ $
negative_passages.docid: 41383
negative_passages.text: Prove that $(x+y+z)^2(yz+zx+xy)^2 \leq 3(y^2+yz+z^2)(z^2+zx+x^2)(x^2+xy+y^2)$
negative_passages.docid: 108995
negative_passages.text: Prove $|e^{i\theta} -1| \leq |\theta|$
negative_passages.docid: 104075
negative_passages.text: Cube roots of the complex numbers 1+i?
negative_passages.docid: 73538
negative_passages.text: solving $\cos z + \sin z = i$
negative_passages.docid: 78712
negative_passages.text: Prove that $\frac{1}{\sin^2 z } = \sum\limits_{n= -\infty} ^ {+\infty} \frac{1}{(z-\pi n)^2} $