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# fp2 complex equation watch

1. 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
2. (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 and you want to find the nth roots of unity, your nth roots of unity will be where Your argument for the complex number doesn't necessarily have to be expressed between -pi and pi
3. (Original post by Felix Felicis)
If you have a complex number and you want to find the nth roots of unity, your nth roots of unity will be where 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?
4. (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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