Conformal Mapping: How Do I Map the Region Above the x-axis?

[atomicpedals]

What I'm trying to do is to apply conformal mapping and map the area bounded by the x-axis and a line at 60 degrees to the x-axis to the region above the x-axis. I think the basic goal of what I'm trying to do is to map \pi/3 to \pi. My problem is I really have no idea where to go from there other than to say I need an expression for w along the lines of w= x² - ( \pi/3 )² + 2i x (\pi/3 ) .

Am I on the right track? What would my next step be?

 

[atomicpedals]

Ok, so sorting through the cloud of my mind the boundary conditions for this case are:

\phi (0,y) = V₁
\phi ( \pi/3 , x) = V₂

 

[grey_earl]

I think you should start in polar coordinates ...

 

[atomicpedals]

So am I mapping from my wedge in polar coordinates (being the area bounded by the x-axis and \pi /3 ) to the line in Cartesian coordinates? And then mapping once more to get from the line to two lines?

 

[grey_earl]

Ok, just forget my remark, I haven't done conformal transformations in a while. Sorry!

 

[atomicpedals]

No worries!