Recent questions in Arc of a Circle

adocidasiaqxm
2022-05-08
Answered

I have not attempted this question and do not understand how to solve this.

Damion Hardin
2022-05-07
Answered

veleumnihryz
2022-05-03
Answered

$f(z)={\displaystyle \frac{z(z-a)}{(z-b)(z-c)(z-d)}}$

be a complex rational function and let $S=\{z\in \mathbb{C}:|z|=1\}$ be the unit circle.

My question:

For which (non-zero complex numbers) $a,b,c$ and $d$ there exist an arc $C$ of $S$ such that $f(C)\subseteq S$ ?

gaitaprepeted05u
2022-05-01
Answered

nrgiizr0ib6
2022-04-30
Answered

Hailee Stout
2022-04-06
Answered

It is asked to prove this theorem without using any notation or any modern form of symbolism whatsoever (algebra). But, to me, this seems to be quite a difficult task. How can this be done?