query: Simplifying $\frac{1}{\sqrt{-1}}$
positive_passages.docid: 3712
positive_passages.text: Why $\sqrt{-1 \cdot {-1}} \neq \sqrt{-1}^2$?
negative_passages.docid: 84597
negative_passages.text: Derivative of $(1-x)^{-2}$
negative_passages.docid: 66082
negative_passages.text: Using $\sqrt{1-t}\leq 1-\frac t2$ to show that $\frac{1\cdot3\cdot5\cdots(2n-1)}{2\cdot4\cdot6\cdots2n}\geq\frac1{2\sqrt n}$
negative_passages.docid: 114861
negative_passages.text: equation $\frac{\frac{1}{x^2}-\frac{1}{y^2}}{\frac{1}{x^2}+\frac{1}{y^2}}$
negative_passages.docid: 35556
negative_passages.text: $f(z)=\frac{z}{1+|z|} $ Is 1-1?
negative_passages.docid: 109540
negative_passages.text: Simplify limit problem $\lim\limits_{x\to 0}\frac{\sqrt{2+x^2}-\sqrt{2+x^2}}{x^2}$
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: 103030
negative_passages.text: Proving $\frac{1}{\sqrt{x}}\ge \frac{2}{x+1}$ for $x> 0$
negative_passages.docid: 131847
negative_passages.text: $\frac{(x-1)(x+1)}{ (x+1)} \rightarrow (x-1)$ Domain Change
negative_passages.docid: 51216
negative_passages.text: Different ways to tackle the integral $\int_0^1\sqrt\frac x{1-x}\,dx$
negative_passages.docid: 132610
negative_passages.text: Expand $\sqrt{1-x}$ up to and including the term $x^2$ (How should i proceed further)
negative_passages.docid: 17707
negative_passages.text: Why is ${x^{\frac{1}{2}}}$ the same as $\sqrt x $?
negative_passages.docid: 117587
negative_passages.text: $\int_{0}^{1}\frac{\sin^{-1}\sqrt x}{x^2-x+1}dx$
negative_passages.docid: 46401
negative_passages.text: Value of $\frac{\sqrt{10+\sqrt{1}}+\sqrt{10+\sqrt{2}}+\cdots+\sqrt{10+\sqrt{99}} }{\sqrt{10-\sqrt{1}}+\sqrt{10-\sqrt{2}}+\cdots+\sqrt{10-\sqrt{99}}}$
negative_passages.docid: 115213
negative_passages.text: How to simplify $\sqrt[3]{7+5\sqrt{2}}+\sqrt[3]{7-5\sqrt{2}}$
negative_passages.docid: 6837
negative_passages.text: How to quotient $\mathbb Z [\sqrt{-11}] / (1+\sqrt{-11})$?
negative_passages.docid: 62055
negative_passages.text: Solve $\frac{d}{dx}f(x)=f(x-1)$