query: $|(z_0-w_1)...(z_0-w_n)|=1$ for some $z_0$ in the unit disk
positive_passages.docid: 27587
positive_passages.text: inequality on the unit disk
negative_passages.docid: 138107
negative_passages.text: Showing that $\left|\frac{z-a}{1-\bar{a}z}\right|=1$
negative_passages.docid: 86535
negative_passages.text: Prove quotient of two $N(0,1)$ is $\text{Cauchy}(0,1)$
negative_passages.docid: 14648
negative_passages.text: Show that $f_0 - f_1 + f_2 - \cdots - f_{2n-1} + f_{2n} = f_{2n-1} - 1$ when $n$ is a positive integer
negative_passages.docid: 104513
negative_passages.text: Order of elements in $Z_n$
negative_passages.docid: 96127
negative_passages.text: Maximum of $|\sin(z)|$ as $\{z: |z| \leq 1 \} $
negative_passages.docid: 57191
negative_passages.text: Show that if $a>e$, the equation $az^n=e^z$ admit $n$ roots in the unit disk - Rouché theorem
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: 82458
negative_passages.text: Homeomorphism between the unit disc and the unit square
negative_passages.docid: 153272
negative_passages.text: Basic question about $\sup_{x\neq 0}{} \frac{\|Ax\|}{\|x\|} = \sup_{\|x\| = 1}{\|Ax\|} $, $x \in\mathbb{R}^n$
negative_passages.docid: 116507
negative_passages.text: Very quick question: function extends to 1/z on the boundary of unit disc
negative_passages.docid: 62901
negative_passages.text: Bound for Analytic Function on Unit Disk
negative_passages.docid: 22586
negative_passages.text: Distribution of $(XY)^Z$ for $(X,Y,Z)$ i.i.d. uniform on $(0,1)$
negative_passages.docid: 60520
negative_passages.text: Upper bound for $|f(0)|$ based on its behavior within the unit disk.
negative_passages.docid: 57816
negative_passages.text: $(S^1 \times [0,1])/\sim$ homeomorphic to unit disk $ D^2$
negative_passages.docid: 43885
negative_passages.text: Proving that $\sum\limits_{n = 0}^{2013} a_n z^n \neq 0$ if $a_0 > a_1 > \dots > a_{2013} > 0$ and $|z| \leq 1$
negative_passages.docid: 38568
negative_passages.text: Finding the number of zeros of $f(z) = z^n$ if $|f(z)| < 1 $ for all $z$ with $|z|=1$.