1. Not finding help here? Sign up for a free 30min 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!

Complex number question

  1. Jul 16, 2006 #1
    Hi, how to solve this question?

    Find the square roots fo the complex number -40-42i.
    (i) Find the square roots of the complex number 40+42i,
    (ii) solve the equation (z+1)^2 + 160 + 168i = 0 for all complex roots.

    I don't know how to start solving this question.
  2. jcsd
  3. Jul 16, 2006 #2


    User Avatar
    Gold Member

    Hello Jack,

    do you know the following representation of a complex number [itex]z[/itex] in the complex plane?

    [tex]z=x+iy=r(\cos\phi+i\,\sin\phi)=r e^{i\phi}[/tex]

    Here's a sketch to clarify what [itex]r[/itex] and [itex]\phi[/itex] are meant to be.



    Last edited: Jul 16, 2006
  4. Jul 17, 2006 #3
    A couple of useful formulas:

    K e^{i\psi} = a + ib \quad
    then \quad
    K = \sqrt{a^2 + b^2} \quad
    \psi = tan^{-1} b/a \quad
    That way you can convert from one form to another. Since taking a square root is easy in the alternative form, you should have no problem.

    This is what nazzard said, but maybe in a manner that is a bit clearer to a beginner in complex numbers. It is really just the application of the pythagorean theorum to the chart above. Compare what I wrote to nazzard's picture. You'll see,

    Last edited: Jul 17, 2006
  5. Jul 17, 2006 #4


    User Avatar
    Gold Member

    Thank you tony. I want to point out that one has to be very careful with using arctan to calculate [tex]\phi[/tex], the so called complex argument of z. Remember: case differentiation for different values of b and a (or y and x in my post).


  6. Jul 17, 2006 #5


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Of course, there's a (possibly) more intuitive and direct way of doing it.

    If sqrt(-40-42i) = (a+bi), then just solve for a and b by squaring both sides (you should be able to fnid two independent equations to break it up into)
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Complex number question