What are some practice questions for conformal mapping involving w=z+b^2/z?

[brandy]

Homework Statement

i have a test comming up soon and i want to study for it but its on conformal mapping and my teacher hasn't given me any examples because he has been away and i can find any questions in any of my textbooks. Basically there is going to be a question on the test involving w=z+b^2/z where z is a complex number and b is a constant.

All is how to take a position on the plane and transform it into a curve. I also know that you can sub in values for w and z (ie u + iv, and a + bi) and rearange to make equal to u and v. but i don't know what to do with it because i haven't had to use it in any questions.

so yea, i was wondering if the kind and incredibly smart brains on physics forums could give me some questions and some answers so that i could get some practise.

 

[lippyka]

Homework Equations w=z+b^2/zThe Attempt at a Solution I'm going to assume that you are familiar with the basic principles of conformal mapping. If so, then here are some simple questions that you can use to practice: 1. Find the image of the point (1,2) under the mapping w=z+b^2/z. Answer: The image of (1,2) is (1 + b^2, 2 + b). 2. Find the inverse mapping of w=z+b^2/z. Answer: The inverse mapping is z = (w - b)/(1 + b^2).