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Math Help - Complex Number Help

  1. #1
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    Complex Number Help

    If the real part of \frac{z+1}{z-1} is zero, find the locus of points representing z in the complex plane.
    Any ideas on what to do first?
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  2. #2
    ixo
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    Since any number divided by zero is undefined and 1-1=0 (the denomitator) makes the equation undefined. Start with the real numbers on either side of it and solve the fraction. test z=0 and z=2 How far apart are they from each other? test a set of numbers closer together say z= .5 and z=1.5 (1.5 is closer to 1 than 2). Are they further apart or closer together than 0 and 2? You have 2 points on the left of zero and 2 on the right of zero so make a line to connect them and see if they ever connect.
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  3. #3
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    Quote Originally Posted by damo17 View Post
    If the real part of \frac{z+1}{z-1} is zero, find the locus of points representing z in the complex plane.
    Any ideas on what to do first?
    Substitute z = x + iy. Then multiply the numerator and denominator by (x - 1) - iy to get the cartesian form. Hence identify the real part.

    So the locus lies on the circle x^2 + y^2 = 1 (but one of the points on this circle is not in the locus ....)
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