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Let f(z) = z + 1/z. Describe the images of both the circle |z| = r or radius r (r ≠ 0) and the ray argz= θ0 under f in terms of well known curves.

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- Mar 9th 2011, 05:54 PMPorter1Describing Circles
Need help describing this problem:

Let f(z) = z + 1/z. Describe the images of both the circle |z| = r or radius r (r ≠ 0) and the ray arg*z*= θ0 under f in terms of well known curves. - Mar 9th 2011, 09:00 PMFernandoRevilla
Express the circle in the form $\displaystyle z=e^{i\theta}\;(\theta\in[0,2\pi])$, the ray in the form $\displaystyle z=\rho e^{i\theta_0}\;(\rho \in[0,+\infty))$ and substitute.