
Jawapan:
Penjelasan:
# 3 + i = sqrt (10) (cos (alpha) + i sin (alpha)) # di mana#alpha = arctan (1/3) #
Jadi
#root (3) (3 + i) = root (3) (sqrt (10)) (cos (alpha / 3) + i sin (alpha / 3)
# = root (6) (10) (cos (1/3 arctan (1/3)) + i sin (1/3 arctan (1/3)) #
# = root (6) (10) cos (1/3 arctan (1/3)) + root (6) (10) sin (1/3 arctan (1/3)
Sejak
Kedua-dua akar kiub lain dari
#omega (root (6) (10) cos (1/3 arctan (1/3)) + root (6) (10) sin (1/3 arctan (1/3)
(6) (10) sin (1/3 arctan (1/3) + (2pi) / 3) i #
# omega ^ 2 (root (6) (10) cos (1/3 arctan (1/3)) + root (6) (10) sin (1/3 arctan (1/3)
(6) (10) sin (1/3 arctan (1/3) + (4pi) / 3) i #