- #1
kjartan
- 15
- 0
Homework Statement
sketch the curve in the z-plane and sketch its image under w=z^2
|z-1|=1
Homework Equations
z=|z|e^(iArgz)
argw=2argz
The Attempt at a Solution
At first I simply sketched the solution for a circle centered at (1,0) in the z-plane and then mapped that to another circle in the w-plane also centered at (1,0). Then I realized that mapping a circle to a circle under the squaring function only works for circles centered at the origin. So, what I have now is sort of ellipse-ish shaped, but I'm not sure how to characterize the solution set in general.
Any help appreciated.