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Thread: Describing Circles

  1. #1
    Junior Member
    Nov 2009

    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.
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
    Nov 2010
    Madrid, Spain
    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.
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