query: An Inequality with complex numbers and $1/\pi$
positive_passages.docid: 45711
positive_passages.text: Inequality with complex numbers
negative_passages.docid: 140599
negative_passages.text: Inequality Proof in Real Numbers: If $p+q=1$ then $pq\le\frac14$
negative_passages.docid: 15237
negative_passages.text: Prove an inequality using complex analysis
negative_passages.docid: 40700
negative_passages.text: Proving inequality $(a+\frac{1}{a})^2 + (b+\frac{1}{b})^2 \geq \frac{25}{2}$ for $a+b=1$
negative_passages.docid: 91131
negative_passages.text: Question regarding an inequality
negative_passages.docid: 151154
negative_passages.text: Prove the inequality $\sqrt\frac{a}{a+8} + \sqrt\frac{b}{b+8} +\sqrt\frac{c}{c+8} \geq 1$ with the constraint $abc=1$
negative_passages.docid: 118884
negative_passages.text: The sine inequality $\frac2\pi x \le \sin x \le x$ for $0<x<\frac\pi2$
negative_passages.docid: 25203
negative_passages.text: with inequality $\frac{y}{xy+2y+1}+\frac{z}{yz+2z+1}+\frac{x}{zx+2x+1}\le\frac{3}{4}$
negative_passages.docid: 147986
negative_passages.text: Prove: if $|z|=1$ than $\frac{z+1}{z-1}$ is an imaginary number
negative_passages.docid: 113993
negative_passages.text: Complex power of a complex number
negative_passages.docid: 92056
negative_passages.text: An inequality on holomorphic functions
negative_passages.docid: 53844
negative_passages.text: How to solve this Complex inequality system
negative_passages.docid: 73771
negative_passages.text: An inequality for a sum of sine functions
negative_passages.docid: 118559
negative_passages.text: Prove the inequality $\sum_{1\le i<j\le n}\sqrt{a_ia_j}<\frac{n-1}2\sum_{i=1}^n a_i$
negative_passages.docid: 68774
negative_passages.text: Proving that $f(x)$ is less than or equal to $1+\pi/4$
negative_passages.docid: 90343
negative_passages.text: Proving the inequality $|e^z-1|\leq e^{|z|}-1$
negative_passages.docid: 158524
negative_passages.text: Complex numbers $z$ such that $|z|= 1$