query: $\tan(\alpha)=\alpha$ has not complex roots?
positive_passages.docid: 29064
positive_passages.text: Can the real and imaginary parts of $\dfrac{\sin z}z$ be simplified?
negative_passages.docid: 150822
negative_passages.text: Finding $\sum_{k=0}^{n-1}\frac{\alpha_k}{2-\alpha_k}$, where $\alpha_k$ are the $n$-th roots of unity
negative_passages.docid: 27278
negative_passages.text: Let $\alpha \in \overline{\Bbb Q}$ a root of $X^3+X+1\in\Bbb Q[X]$. Calculate the minimum polynomial of $\alpha^{-1}$ en $\alpha -1$.
negative_passages.docid: 90475
negative_passages.text: Coordinate-free proof of $\operatorname{Tr}(AB)=\operatorname{Tr}(BA)$?
negative_passages.docid: 131701
negative_passages.text: Why is $A^TA$ invertible if $A$ has independent columns?
negative_passages.docid: 78561
negative_passages.text: Algebraic field extensions: Why $k(\alpha)=k[\alpha]$.
negative_passages.docid: 88474
negative_passages.text: $\mathbb{A}^{2}$ not isomorphic to affine space minus the origin
negative_passages.docid: 24656
negative_passages.text: Proving that $\frac{\csc\theta}{\cot\theta}-\frac{\cot\theta}{\csc\theta}=\tan\theta\sin\theta$
negative_passages.docid: 120213
negative_passages.text: Example $x$, $y$ and $z$ values for $x\uparrow^\alpha y=z$ where $\alpha\in \Bbb R-\Bbb N$
negative_passages.docid: 9539
negative_passages.text: $\alpha$ and $\beta$ are solution of $a \cdot \tan\theta + b \cdot \sec\theta = c$ show $ \tan(\alpha + \beta) = \frac{2ac}{a^2 - c^2}$
negative_passages.docid: 100907
negative_passages.text: $\sin\alpha + \sin\beta + \sin\gamma = 4\cos{\frac{\alpha}{2}}\cos{\frac{\beta}{2}}\cos{\frac{\gamma}{2}}$ when $\alpha + \beta + \gamma = \pi$
negative_passages.docid: 51647
negative_passages.text: Proof that a trigonometric function of a rational angle must be non-transcendental
negative_passages.docid: 1914
negative_passages.text: General way to determine $\mathbb{Q}(\gamma) = \mathbb{Q}(\alpha,\beta)$ given $\alpha$ and $\beta$
negative_passages.docid: 154172
negative_passages.text: Finding $\tan t$ if $t=\sum\tan^{-1}(1/2t^2)$
negative_passages.docid: 72201
negative_passages.text: How can we plot the complex roots of an equation?
negative_passages.docid: 51314
negative_passages.text: How to prove that a complex number is not a root of unity?
negative_passages.docid: 157200
negative_passages.text: Roots of a equation on a complex plane