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: 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


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Change it back to a+bi form using m=0,1,2 .
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook