MAT334-2018F > End of Semester Bonus--sample problem for FE

FE Sample--Problem 4

(1/1)

Victor Ivrii:
(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 $z$.

Yilin Wang:
solution for part a, b and c