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Show z^2 maps the circle |z-1|=1 to a cardioid

  1. Apr 11, 2009 #1
    1. The problem statement, all variables and given/known data
    show z^2 maps the circle |z-1|=1 to a cardioid 2(1+cos(theta))e^(i*theta)

    2. Relevant equations

    3. The attempt at a solution
    I tried using the restriction |z-1| = 1 and simply got that r^2=2x.

    Then I tried to apply that and got


    I've been trying for a good 15 minutes.
  2. jcsd
  3. Apr 11, 2009 #2
    NVM, take z = 1+cos +isin
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