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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

    [tex]177147(8.19..+7.33..i)[/tex]

    [tex]1452413.3..+1299078i[/tex]



    hope that's right :D

    thnx
     
  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

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Why not just sin-1(-2/3)? (Admittedly, that is the same as 360- sin-1(2/3).)
     
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