query: Need help with proof with absolute value and complex numbers.
positive_passages.docid: 144521
positive_passages.text: Why does Möbius transformation $f(z)$ map the unit disk $|z|<1$ to itself?
negative_passages.docid: 119628
negative_passages.text: Proving an identity relating to the complex modulus: $z\bar{a}+\bar{z}a \leq 2|a||z|$
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: 143248
negative_passages.text: What approach should I take to establish this logical proof?
negative_passages.docid: 118981
negative_passages.text: Proving $\sqrt{ab} = \sqrt a\sqrt b$
negative_passages.docid: 2251
negative_passages.text: Can someone give me a hint on how to prove this?
negative_passages.docid: 1859
negative_passages.text: Proving $\arctan(\sqrt{x^2+1}-x)=\frac{\pi}{4}-\frac{1}{2}\arctan(x)$
negative_passages.docid: 81775
negative_passages.text: Prove $a^\alpha b^{1-\alpha} \le \alpha a + (1 - \alpha)b, \; a,b > 0,\; 0 < \alpha < 1$
negative_passages.docid: 103536
negative_passages.text: How to prove $|e^{i\theta} - 1| \leq |\theta|$?
negative_passages.docid: 81571
negative_passages.text: Complex Exponent of Complex Numbers
negative_passages.docid: 29276
negative_passages.text: technique of proving continuity complex function
negative_passages.docid: 79425
negative_passages.text: Prove the direct product of nonzero complex numbers under multiplication.
negative_passages.docid: 45711
negative_passages.text: Inequality with complex numbers
negative_passages.docid: 155572
negative_passages.text: How to prove that at least one of the absolute values of sin(n) , sin(n+1)),sin(n+2) is greater than 0.5
negative_passages.docid: 39779
negative_passages.text: If $a,b,c>0$ and $a+b+c=1$, prove that $\sqrt{\frac{ab}{c+ab}}+\sqrt{\frac{bc}{a+bc}}+\sqrt{\frac{ac}{b+ac}} \le \frac{3}{2}$.
negative_passages.docid: 48038
negative_passages.text: If $z$ and $w$ are complex numbers such that $|(z+w)| = |(z-w)|$, prove that $\arg(z)-\arg(w) = \pm (\pi/2)$
negative_passages.docid: 31783
negative_passages.text: Is this proof of $ab = 0$ correct?