- #1
latentcorpse
- 1,444
- 0
Let [itex]L:=\{z:|z-1|<1\} \cap \{z:|z-i|<1\}[/itex]. Find a Mobius transformation that maps L onto the sector [itex]\{z: 0< arg(z) < \alpha \}. What is the angle [itex]\alpha[/itex]?
no idea of how about to set up the problem
The intersection of the two circles forms a lens shaped region L with boundary curves, let's call them [itex]C_1[/itex] and [itex]C_2[/itex].
i couldn't decide whether to write down a generic Mobius transformation [itex]f(z)=\frac{az+b}{cz+d}[/itex] and try and work with it (this would need me to define stuff like points that map to zero and infinity though would it not) or to use the fact that Mobius transformations are combinations of inversions, dilations, rotations and translations and try and sipmlify the Mobius transformation this way?
i need some explanation...
cheers
no idea of how about to set up the problem
The intersection of the two circles forms a lens shaped region L with boundary curves, let's call them [itex]C_1[/itex] and [itex]C_2[/itex].
i couldn't decide whether to write down a generic Mobius transformation [itex]f(z)=\frac{az+b}{cz+d}[/itex] and try and work with it (this would need me to define stuff like points that map to zero and infinity though would it not) or to use the fact that Mobius transformations are combinations of inversions, dilations, rotations and translations and try and sipmlify the Mobius transformation this way?
i need some explanation...
cheers