1. The problem statement, all variables and given/known data
Find function that maps area between ##|z|=2## and ##|z+1|=1## on area between two parallel lines.
2. Relevant equations
3. The attempt at a solution
I don't know how to check if my solution works for this problem?
I used Möbious transformation:
##f(z)=\frac{az+b}{cz+d}## where I decided that ##f(-2i)=\infty ## and ##f(2i)=0## and ##f(2)=2i##.
Using this I find out that ##f(z)=\frac{(z-2i)(i-4)}{\frac{1-i}{2}z+i+1}##
Now I am almost 100% if the circles would both have center in point 0. However, they have different origins and I somehow don't know how to deal with this kind of problems. :(
Find function that maps area between ##|z|=2## and ##|z+1|=1## on area between two parallel lines.
2. Relevant equations
3. The attempt at a solution
I don't know how to check if my solution works for this problem?
I used Möbious transformation:
##f(z)=\frac{az+b}{cz+d}## where I decided that ##f(-2i)=\infty ## and ##f(2i)=0## and ##f(2)=2i##.
Using this I find out that ##f(z)=\frac{(z-2i)(i-4)}{\frac{1-i}{2}z+i+1}##
Now I am almost 100% if the circles would both have center in point 0. However, they have different origins and I somehow don't know how to deal with this kind of problems. :(
0 commentaires:
Enregistrer un commentaire