Tricky complex numbers question

  1. 1. The problem statement, all variables and given/known data
    Harder: given that
    √(−15 − 8i) = ±(1 − 4i) obtain the two solutions of the equation
    z² + (−3 + 2i)z + 5 − i = 0


    2. Relevant equations

    I can easily prove √(−15 − 8i) = ±(1 − 4i) but that's not important

    3. The attempt at a solution

    I would of thought that a compex solution would be a + b and a - b, but a quick glance at the answers shows 2 completely different complex numbers - no complex conjugates.

    Well seperating the equation into real and imaginary parts then solving for z:
    real:
    (z² - 3z + 5) = 0
    => [tex] z = \frac{3\pm i \sqrt{11}}{2}[/tex]

    imag:
    (2z - 1) = 0
    => z = 0.5

    This isn't taking me anywhere nice...

    Ideas!? :)

    Thanks
     
  2. jcsd
  3. Dick

    Dick 25,620
    Science Advisor
    Homework Helper

    You can't separate it into real and imaginary parts like that, z itself is probably complex. Just use the quadratic formula on the original equation.
     
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