I need a help in solving the following problem. the problem says: find the image of the unit circle |z|=1, under the mapping w=2z+z^2.
Given a point on the unit circle, it will have the form where . Have: .
This means that the real part is and the imaginary part is . These are the parametric equations of a cardioid. You can take several values of t and try to draw it.
Cardioid - Wikipedia, the free encyclopedia