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Math Help - Complex plane problem

  1. #1
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    Complex plane problem

    Sketch {z E C : |z - 1| + |z + 1| = 4}

    Attempt:

    |z - 1| + |z + 1| = 4
    |x + yi - 1| + |x + yi + 1| = 4
    \sqrt{(x - 1)^2 + y^2} + \sqrt{(x + 1)^2 + y^2} = 4
    \sqrt{x^2 - 2x + 1 + y^2} + \sqrt{x^2 + 2x + 1 + y^2} = 4

    I tried squaring both sides to get rid of the square root on the LHS, but this made things more complicated. Is there a simpler way?
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  2. #2
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