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Graphing the image of a complex number

  1. Jan 12, 2009 #1
    1. The problem statement, all variables and given/known data

    sketch y=2 under the image w=z^(2)

    2. Relevant equations

    3. The attempt at a solution
    z=x+(1)i=x+i {y=1 and x can be anything}

    after regrouping, w=(x^2-1)+(2x)i and then I consider x^2-1 to be the real part and 2x to be the imaginary part. This is as far as I can get because I have no clue how to graph this.
  2. jcsd
  3. Jan 12, 2009 #2


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    I think you just confused because there are a couple of different meanings of x around. Try it this way (if you mean y=1 and not y=2 as you posted). A general point on the line y=1 is given (as you said) by t+i where t is any number. Squaring gives x=t^2-1 and y=2t splitting real and imaginary parts. Solve the y equation for t and substitute into the x equation to get an equation involving only x and y.
  4. Jan 13, 2009 #3
    Ok so I just put x=t^2-1 and y=2t. From this I can conclude that t=y/2 and that x=(y^4)/4-1. This is just a parabola opening to the right facing in the x direction. Is this correct?
  5. Jan 13, 2009 #4


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    Sounds correct to me. You did mean x=y^2/4-1, right?
  6. Jan 13, 2009 #5
    lol yeah.
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