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Math Help - Complex numbers problem

  1. #1
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    Complex numbers problem

    Let z be a complex number represented by  x +iy What is the condition for the relationship between x and y such that \frac {z}{1+z^2} is a real number? A. xy=1 B. x=y C. x^2 -y^2 =1 D. x^2 + y^2 =1 E. none of them above
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  2. #2
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    Re: Complex numbers problem

    Quote Originally Posted by shiny718 View Post
    Let z be a complex number represented by  x +iy What is the condition for the relationship between x and y such that \frac {z}{1+z^2} is a real number? A. xy=1 B. x=y C. x^2 -y^2 =1 D. x^2 + y^2 =1 E. none of them above
    I can tell you that the correct answer is D.
    If one makes all the conversions to rectangular form, its easy to see that if y-y^3-x^2y=0 the fraction is real.
    That is the same as y(1-y^2-x^2)=0 thus the answer is x^2+y^2=1.
    It should be noted that if y=0 is also a solution.

    I will not do the algebra.
    Thanks from shiny718
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