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Homework Help: Find no. of Complex Numbers

  1. Oct 3, 2012 #1


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    Gold Member

    1. The problem statement, all variables and given/known data
    Find the number of complex numbers satisfying [itex] |z|=z+1+2i[/itex]

    2. Relevant equations

    3. The attempt at a solution
    Let z=x+iy
    |x+iy| = (x+1)+i(2+y)
    Squaring and taking modulus
    |[itex]\sqrt{x^{2}+y^{2}}|^{2} = |(x+1)+i(2+y)|^{2}[/itex]
    [itex]x^{2}+y^{2} = (x+1)^{2}+(2+y)^{2}[/itex]
    Rearranging and simplifying I get

    Now what to do next? Also Is there any other way to solve this question?
  2. jcsd
  3. Oct 3, 2012 #2


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    Science Advisor

    You seem to have missed an important point- the absolute value of a complex number is real. Since the left side of the equation is real, the right side must be. z must be of the form z= x- 2i so that z+ 1+ 2i= x+1. What you did was correct but how many points on the line 2x+ 4y+ 5= 0 also satisfy y= -2?
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