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Power of complex number

  1. Nov 16, 2009 #1
    how to find number [tex](3-i)^{12}[/tex] ?

    i know theorem for powers of complex numbers, but i have to know argument of trygonometrical form.

    and its [tex] cos x = 3/4[/tex] and [tex]sin x = -1/4[/tex]

    and i dont know what to do with that.
  2. jcsd
  3. Nov 16, 2009 #2
    First write [itex]3 - i [/itex] in the form [itex]r (\cos\theta + i \sin \theta)[/itex] . Then [itex](3 - i)^{12} [/itex] will be [itex]r^{12} (\cos(12 \theta) + i \sin (12 \theta))[/itex]
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