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    solve z^5 = 4 + 4i, giving answers in the form z=e^( ik(pi) ) where k is rational and 0<=k<=2

    why are some answers of theta out of the range -pi<theta<=pi ?
    i dont get it
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    (Original post by cooldudeman)
    solve z^5 = 4 + 4i, giving answers in the form z=e^( ik(pi) ) where k is rational and 0<=k<=2

    why are some answers of theta out of the range -pi<theta<=pi ?
    i dont get it
    If you have a complex number r e^{i \theta + 2 \pi k} and you want to find the nth roots of unity, your nth roots of unity will be r^{1/n} e^{\frac{i \theta + 2 \pi k}{n}} where 0 \leq k \leq (n-1) Your argument for the complex number doesn't necessarily have to be expressed between -pi and pi
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    (Original post by Felix Felicis)
    If you have a complex number r e^{i \theta + 2 \pi k} and you want to find the nth roots of unity, your nth roots of unity will be r^{1/n} e^{\frac{i \theta + 2 \pi k}{n}} where 0 \leq k \leq (n-1) Your argument for the complex number doesn't necessarily have to be expressed between -pi and pi
    so you just keep adding 2pi until you have 'n' amount of answers?

    and how do you know whether or not you have negative answers of theta?
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    (Original post by cooldudeman)
    so you just keep adding 2pi until you have 'n' amount of answers?
    Yes, but you go up to (n-1) as you start with k=0.
 
 
 
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