# Describing Circles

• March 9th 2011, 05:54 PM
Porter1
Describing 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.
• March 9th 2011, 09:00 PM
FernandoRevilla
Express the circle in the form $z=e^{i\theta}\;(\theta\in[0,2\pi])$, the ray in the form $z=\rho e^{i\theta_0}\;(\rho \in[0,+\infty))$ and substitute.