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Find all the values of (-2+2i)^(1/3)

  1. Oct 4, 2011 #1
    1. The problem statement, all variables and given/known data

    Find all the values of (-2+2i)1/3

    2. Relevant equations

    eib = cos(b) + i * sin(b)

    3. The attempt at a solution

    (-2+2i)1/3 = (2(-1+i))1/3 = 21/3 (√2)1/3 (eiπ(3/4 + 2m))1/3 = 21/2 (eπi)1/4 + 2m/3 = ....... Where am I going with this? I don't even know.
  2. jcsd
  3. Oct 4, 2011 #2
    You need to use the definition:

    [tex]u^{1/n}=|u|^{1/n} e^{i/n(\theta+2n\pi i)}[/tex]

    where [itex]\theta[/itex] is the argument of u
  4. Oct 4, 2011 #3


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    Change it back to a+bi form using m=0,1,2 .
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