Find all the complex cube roots of w 64 cos 150 degree i s

Find all the complex cube roots of w = 64 (cos 150 degree + i sin 150 degree). Write the roots in polar form with theta in degrees. z_0 = (cos degree + i sin degree) (Type answers in degrees. Simplify your answer.) z_1 = (cos degree + i sin degree) (Type answers in degrees. Simplify your answer.) z_2 = (cos degree + i sin degree) (Type answers in degrees. Simplify your answer.)

Solution

given w=64(cos150^o+i sin150^o)

w=z³

z³=64(cos150^o+i sin150^o)

z₀=(64(cos150^o+i sin150^o))^1/3,z₁=(64(cos(360+150)^o+i sin(360+150)^o))^1/3,z₂=(64(cos(720+150)^o+i sin(720+150)^o))^1/3

z₀=64^1/3(cos150^o+i sin150^o)^1/3,z₁=64^1/3(cos(510)^o+i sin(510)^o))^1/3,z₂=64^1/3(cos(870)^o+i sin(870)^o)^1/3

z₀=4(cos(150_/3)^o+i sin(150_/3)^o),z₁=4(cos(510_/3)^o+i sin(510_/3)^o)),z₂=4(cos(870_/3)^o+i sin(870_/3)^o)

z₀=4(cos(50)^o+i sin(50)^o),z₁=4(cos(170)^o+i sin(170)^o)),z₂=4(cos(290)^o+i sin(290)^o)