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: Complex number calculation

  1. Jul 4, 2007 #1
    not sure if this is in the right section as i havn't got to calculus yet lol. anyways, was wondering whether you could check i have calculated this right as I'm learning complex numbers at the moment and have no way of checking my working. thnx

    1. The problem statement, all variables and given/known data

    Calculate [tex](\surd5 - 2i)^{11}[/tex]

    2. Relevant equations

    3. The attempt at a solution

    Find polar form of [tex](\surd5 - 2i)[/tex]

    [tex]r = complex modulus[/tex]

    [tex]r = \sqrt{5 + 4}[/tex]
    [tex]r = 3[/tex]

    [tex]Arg(z) = sin^{-1}(\frac{2}{3})[/tex]

    sub all that into [tex]r(cosArg(z) + i*sinArg(z))[/tex]

    but before actual calculate take the power of 11 into consideration so...

    [tex](\surd5 - 2i)^{11} = r^{11}(11*cosArg(z) + 11i*sinArg(z))[/tex]

    I then calculate all that as



    hope that's right :D

  2. jcsd
  3. Jul 4, 2007 #2
    The argument of a complex number (x+iy) = ????
  4. Jul 4, 2007 #3
    ermmm, did i just work out the angle of the triangle instead of working out the angle counterclockwise from the x-axis? (on the argand diagram i think its called/complex plane)

    think i might of

    would the arguement be instead [tex]360 - sin^{-1}(\frac{2}{3})[/tex]?
  5. Jul 4, 2007 #4


    User Avatar
    Science Advisor

    Why not just sin-1(-2/3)? (Admittedly, that is the same as 360- sin-1(2/3).)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook