Math Help - Describing Circles

1. 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.

2. 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.