Double Check My Conformal Mapping Steps for Quarter-Plane

[elimenohpee]

Homework Statement

Can someone double check my mapping steps I've taken?

The domain includes the quarter-plane Re(z)>0 and Im(z)>0, with a branch cut from the origin to the point [tex]\sqrt{3}[/tex]exp(pi*i/4)

The Attempt at a Solution

I want to map the region from the quarter-plane to the upper half plane Im(z)>0

To start this, I send the right most point of the branch cut to infinity by the transformation:

w1 = (z) / ( [tex]\sqrt{3}[/tex] - z)

does this make the branch cut lie from 0 -> infinity?

Then to send the quarter plane to the upper half plane, just square the previous transformation:

w2 = (w1)^2

 

[mighty2000]

= (z) / ( \sqrt{3} - z)^2



it is important to always double check your work and make sure that your steps and calculations are correct. In this case, it seems like you have correctly mapped the quarter-plane to the upper half plane by sending the rightmost point of the branch cut to infinity and then squaring the transformation. However, it is always a good idea to double check your work by plugging in different points and making sure they are correctly mapped. Additionally, it may be helpful to graph the original and transformed regions to visually confirm the mapping. Keep up the good work!