Toronto Math Forum
MAT3342018F => MAT334Tests => End of Semester Bonussample problem for FE => Topic started by: Victor Ivrii on November 27, 2018, 03:57:15 AM

(a) Find the Mobius's transformation $f(z)$ mapping the unit disk $\{z\colon z<1\}$ onto exterior $\{w\colon w>1\}$ of the unit disk, such that $f(0)=5$ and $f(1)=1$.
(b) Find the fixed points of $f$ (points s.t. $f(z)=z$).
(c) Find the stretch ($f'(z)$) and the rotation angle ($\arg(f'(z))$) of $f$ at $z$.

solution for part a, b and c