query: Find the minimum value of the expression $|z|^2 +|z-3|^2 +|z-6i|^2$
positive_passages.docid: 24221
positive_passages.text: Complex numbers - minimum value proof
negative_passages.docid: 53411
negative_passages.text: Minimum of $\sqrt{\frac{a}{b+c}}+\sqrt{\frac{b}{c+a}}+\sqrt{\frac{c}{a+b}}$
negative_passages.docid: 117970
negative_passages.text: Find the minimal polynomial for $\sqrt[3]{2} + \sqrt[3]{4}$ over $\mathbb{Q}$
negative_passages.docid: 103310
negative_passages.text: Evaluation of the following expression
negative_passages.docid: 96927
negative_passages.text: Modus Operandi. Formulae for Maximum and Minimum of two numbers with a + b and $|a - b|$
negative_passages.docid: 33199
negative_passages.text: Least value of an Expression?
negative_passages.docid: 96875
negative_passages.text: Finding the value of $x^{x^2}+x^{x^6}$ given that $x^{x^4}=4$
negative_passages.docid: 125096
negative_passages.text: Minimal polynomial of $\alpha=\sqrt 2e^\frac{2\pi i}{3}$
negative_passages.docid: 90933
negative_passages.text: Finding the roots of complex numbers
negative_passages.docid: 37650
negative_passages.text: Find $\sum_{m=0}^n\ (-1)^m m^n {n \choose m}$
negative_passages.docid: 7066
negative_passages.text: Calculate simple expression: $\sqrt[3]{2 + \sqrt{5}} + \sqrt[3]{2 - \sqrt{5}}$
negative_passages.docid: 131168
negative_passages.text: Minimizing $\cot^2 A +\cot^2 B + \cot^2 C$ for $A+B+C=\pi$
negative_passages.docid: 48154
negative_passages.text: Find the minimum value of $f(x,y,z)=\frac{x^2}{(x+y)(x+z)}+\frac{y^2}{(y+z)(y+x)}+\frac{z^2}{(z+x)(z+y)}$.
negative_passages.docid: 115229
negative_passages.text: Find the zeros of $h(z)=z^6-5z^4+3z^2-1$ within the unit disc - Verification
negative_passages.docid: 13220
negative_passages.text: find the minimum value of $\frac{a}{b}+\frac{b}{c}+\frac{c}{a}$
negative_passages.docid: 99930
negative_passages.text: Find the Maximum value of $\frac{x}{\sqrt{x+y}}+\frac{y}{\sqrt{y+z}}+\frac{z}{\sqrt{z+x}}$
negative_passages.docid: 73538
negative_passages.text: solving $\cos z + \sin z = i$