Hi i need help for calcul:
( 1/2 ( -1 + i√3 )) ^3
and
( 1/2 ( -1 - i√3 )) ^3
thanks for your help
use de Moivre's theorem
= (1/8) (-1+√3i)^3
let's just concentrate on the -1+√3
magnitude = √4 = 2
so
-1 + √3 = 2(cosØ + isinØ)
where tanØ = -√3/1 , Ø = 120°
so -1 + √3 = 2(cos120 + i sin120°)
then by De Moivre's theorem
(-1+√3)^3 = 2^3 (cos 360 + i sin360)
= 8(1 +0)
= 8
so (1/8)(-1+i√3)^3
= (1/8)(8)
= 1
do the same with your second question, (your angle will be
240°)