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Complex plane locus question (another one!)

  1. Mar 22, 2014 #1
    1. The problem statement, all variables and given/known data

    again there is no answer provided in the book!

    a +bt +ct^2 = z where t is a real parameter, and a, b, c are complex numbers with b/c real


    2. Relevant equations

    3. The attempt at a solution

    b/c real indicates that b and c are pure imaginary so when you split the equation into real and imaginary parts:

    x = Re(a)

    y = Im(a) + Im(b)t + Im(c)t^2

    since t is a parameter, in the complex plane, the locus of z is a straight vertical line with x = Re(a)?
     
  2. jcsd
  3. Mar 22, 2014 #2
    Are you sure? What if b = 1 + i and c = 2 + 2i ?
     
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