Asked by Sébastien
Hi i need help for calcul with a Moivre's theorem:
( 1/2 ( -1 - i√3 )) ^3
thanks for your help
( 1/2 ( -1 - i√3 )) ^3
thanks for your help
Answers
Answered by
Steve
convert (x,y) to (r,θ)
1/2 ( -1 - i√3 ) = (1,4π/3)
(re<sup>iθ</sup>)<sup>n</sup> = r<sup>n</sup>e<sup>inθ</sup>
(1,4π/3)<sup>3</sup> = (1<sup>3</sup>,4π) = (1,4π)
in (x,y) that's (1,0)
1/2 ( -1 - i√3 ) = (1,4π/3)
(re<sup>iθ</sup>)<sup>n</sup> = r<sup>n</sup>e<sup>inθ</sup>
(1,4π/3)<sup>3</sup> = (1<sup>3</sup>,4π) = (1,4π)
in (x,y) that's (1,0)
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