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Complex numbers (2)

  1. Sep 11, 2009 #1
    hey again,

    im have a problem with 1 of the questions im doing.

    Z^3 = 2+2i, and it asks to solve for Z.

    does it want me to actually get a number for Z? or does it simply want me to write....

    z = (2+2i)^(1/3)

    but ^^^^ this seems way to easy
     
  2. jcsd
  3. Sep 11, 2009 #2
    Well... Using De Moivre's theorem, there are actually 3 solutions for that equation.

    Because 2 + 2i can be expressed as 2[tex]\sqrt{2}[/tex]ei([tex]\pi[/tex]/4) = 2[tex]\sqrt{2}[/tex]ei([tex]\pi[/tex]/4+2k[tex]\pi[/tex]).

    so Z3 = 2[tex]\sqrt{2}[/tex]ei([tex]\pi[/tex]/4+2k[tex]\pi[/tex])

    => Z = (2[tex]\sqrt{2}[/tex]ei([tex]\pi[/tex]/4+2k[tex]\pi[/tex]))(1/3) for any 3 consecutive values of k.
     
  4. Sep 11, 2009 #3

    lurflurf

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    Poorly written instructions perhaps. You could write Z in a+ib form.
     
  5. Sep 11, 2009 #4
    thanks repainted, lurflurf how could i rearange it so that its in a + ib form?
     
  6. Sep 11, 2009 #5

    rock.freak667

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    Use Euler's formula of e=cosθ+isinθ
     
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