1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 2nd degree equation (complex numbers)

  1. Aug 22, 2007 #1
    I just came across the eq.

    z^2 - 2z + 1 - 2i

    where z is a complex number. How do I solve this sort of eq.?

    I tried to solve it as a normal 2nd degree eq., setting a=2, b=-2 and c=(1-2i), with z as the variable. This finally gave me the solutions

    z(1) = -1 + sqrt(2i)


    z(2) = -1 - sqrt(2i)

    Can this be the correct solution? I had hoped for an answer involving i, not sqrt(i)...
  2. jcsd
  3. Aug 22, 2007 #2
    This is correct -- though you might want to find the solution to [tex]a+b i = \sqrt{i}[/tex] where a and b are real numbers. Remember that the point of the complex numbers to to be closed under things like taking square roots.
  4. Aug 22, 2007 #3
    A relevant equation might be
    [tex]\left( \frac{1}{\sqrt{2}} + \frac{i}{\sqrt{2}}\right)^2 = i[/tex]

    which can be found graphically by viewing the unit circle [tex]|z|=1[/tex] in the complex plane, and considering that if [tex]z = |z|_{\theta}[/tex], then [tex]z^n = |z|^n _{n \theta}[/tex], where [tex]\theta[/tex] is the angle between the lines corresponding to [tex]z[/tex] and [tex]1+0i[/tex].
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook