Equality holds only when z is real or pure imaginary, which are all the points on the real and imaginary axis. We have. Solution Recall that a circle in R2 centered at a; b with radius r is given by the equation. Thus our equation becomes.
Instructor : Nikhil Srivastava , email: firstname at math. Supplementary Text : Gamelin, Complex Analysis. Available online for Berkeley students at Springerlink. Syllabus : We will cover the first 9 chapters of Brown and Churchill and some additional topics, such as infinite products and applications of conformal mapping.