List questions from rouches-theorem | MathQA

Find how many solutions (counting multiplicity) the equation $\sin z = ez^4$ has on the unit disk $|z|<1$.

Published on 16 Jul 2022 - 17:49

What is the number of zeros of the this polynomial?

Published on 25 Jul 2022 - 1:57

Suppose $f(z)$ is analytic on $|z|<1$ such that $|f(z)|<1$ for all $|z|<1$ and $f(0) = \alpha \neq 0$. Show $f(z) \neq 0$ for all $|z|<|\alpha|$.

Published on 01 Aug 2022 - 18:09

Show that all the roots of $p(z)= z^5 – z^3 + 1$ are in the ring $\frac{1}{2}\lt \vert z \vert \lt \frac{3}{2}$.

Published on 09 Aug 2022 - 23:55

How to obtain the relationship between a plane and a line in $\mathbb{R}^3$

Published on 08 Sep 2022 - 11:27

Rouché Theorem Application

Published on 29 Nov 2022 - 7:48

Rouché's theorem proof question

Published on 08 Dec 2022 - 14:37

Rouches proof question regarding the curve $\gamma$

Published on 02 Jan 2023 - 13:34