1. ## Mapping

Hi

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.

Thanks

2. Given a point on the unit circle, it will have the form $z=e^{(it)}$ where $0\leq t \leq 2\pi$. Have: $w=2z+z^2 = 2e^{(it)}+e^{(2it)}$.
This means that the real part is $x=2cos(t)+cos(2t)$ and the imaginary part is $y=2sin(t)+sin(2t)$. 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

3. Thanks Mr. Fawwaz I have reached x and y but I did not know how to proceed.