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

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- Mar 10th 2011, 12:25 AMmia25Mapping
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 - Mar 10th 2011, 01:35 AMmohammadfawaz
Given a point on the unit circle, it will have the form $\displaystyle z=e^{(it)}$ where $\displaystyle 0\leq t \leq 2\pi$. Have: $\displaystyle w=2z+z^2 = 2e^{(it)}+e^{(2it)}$.

This means that the real part is $\displaystyle x=2cos(t)+cos(2t)$ and the imaginary part is $\displaystyle y=2sin(t)+sin(2t)$. 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 - Mar 10th 2011, 01:52 AMmia25
Thanks Mr. Fawwaz I have reached x and y but I did not know how to proceed.