query: How to prove this inequality of bounded complex number.?
positive_passages.docid: 29198
positive_passages.text: How to prove the following inequality $|\prod_{i=1}^{i=n}a_i-\prod_{i=1}^{i=n}b_i| < n\delta$?
negative_passages.docid: 146885
negative_passages.text: How prove this inequality $\frac{a-b}{b+c}+\frac{b-c}{c+d}+\frac{c-d}{d+e}+\frac{d-e}{e+a}+\frac{e-a}{a+b}\ge 0$
negative_passages.docid: 89509
negative_passages.text: Suppose $z \neq -1$ is a complex number of norm 1. Prove that $(\frac{1+z}{|1+z|})^2 =z $
negative_passages.docid: 115335
negative_passages.text: How can we prove this integral inequality?
negative_passages.docid: 88687
negative_passages.text: Proof of the inequality $||a+b|^p - |a|^p| \leq \epsilon |a|^p + C_{\epsilon} |b|^p$
negative_passages.docid: 128189
negative_passages.text: Proving Integral Inequality
negative_passages.docid: 58969
negative_passages.text: A proof for the inequality $\sum_{i=0}^{t-2}{\frac{1}{t+3i}} \leq \frac{1}{2} $ for all $t \geq 2$
negative_passages.docid: 30330
negative_passages.text: How can I prove that this function is bounded using the given 2 hints?
negative_passages.docid: 73987
negative_passages.text: Prove the inequality $({1+\frac{a}b})^n$ + $(1+\frac{b}a)^n$ $\geq$ $2^{n+1}$
negative_passages.docid: 137718
negative_passages.text: Prove that the complex expression is real
negative_passages.docid: 147986
negative_passages.text: Prove: if $|z|=1$ than $\frac{z+1}{z-1}$ is an imaginary number
negative_passages.docid: 118613
negative_passages.text: Proving an inequality: $|1-e^{i\theta}|\le|\theta|$
negative_passages.docid: 29276
negative_passages.text: technique of proving continuity complex function
negative_passages.docid: 52204
negative_passages.text: Proof of one inequality $a+b+c\leq\frac{a^3}{bc}+\frac{b^3}{ca}+\frac{c^3}{ab}$
negative_passages.docid: 95266
negative_passages.text: Show $|t|\leq \pi \Rightarrow |e^{it}-1|\geq 2|t|/ \pi$
negative_passages.docid: 136721
negative_passages.text: Absolute value of a complex number proof
negative_passages.docid: 129890
negative_passages.text: Proving inequality $|\sin(n\theta) |\le n\sin\theta$