# Toronto Math Forum

## MAT334-2018F => MAT334--Tests => End of Semester Bonus--sample problem for FE => Topic started by: Victor Ivrii on November 27, 2018, 03:57:15 AM

Title: FE Sample--Problem 4
Post 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 $z$.
Title: Re: FE Sample--Problem 4
Post by: Yilin Wang on November 30, 2018, 12:41:13 AM
solution for part a, b and c