query: Complex number moduli inequalities
positive_passages.docid: 6100
positive_passages.text: Show that $\left|\frac{\alpha - \beta}{1-\bar{\alpha}\beta}\right| < 1$ when $|\alpha|,|\beta| < 1$
negative_passages.docid: 95081
negative_passages.text: Ordering on complex numbers
negative_passages.docid: 140968
negative_passages.text: Proof for Property of Complex Numbers
negative_passages.docid: 63255
negative_passages.text: Proving an entire, complex function with below bounded modulus is constant.
negative_passages.docid: 26501
negative_passages.text: Proof using complex numbers
negative_passages.docid: 92595
negative_passages.text: A problem regarding the in-equality of complex numbers .
negative_passages.docid: 16852
negative_passages.text: $|e^a-e^b| \leq |a-b|$ for complex numbers with non-positive real parts
negative_passages.docid: 14668
negative_passages.text: complex number question involving modulus
negative_passages.docid: 66261
negative_passages.text: Inequalities help: $(a^3+b^3)^2\leq (a^2+b^2)(a^4+b^4)$
negative_passages.docid: 116206
negative_passages.text: Complex number question on proving an inequality.
negative_passages.docid: 28854
negative_passages.text: Modulus with a negative number
negative_passages.docid: 118244
negative_passages.text: An $n$th root inequality: $\sqrt[n]{n} < 1 + \sqrt{2/n}$
negative_passages.docid: 112348
negative_passages.text: Defining the Complex numbers
negative_passages.docid: 81150
negative_passages.text: Positive integer multiples of an irrational mod 1 are dense
negative_passages.docid: 74024
negative_passages.text: Higher dimensional equivalent of complex numbers
negative_passages.docid: 71540
negative_passages.text: Real and Imaginary Parts of tan(z)
negative_passages.docid: 61262
negative_passages.text: Is $\cot(z)-\frac1z$ bounded on a given circle?