Application of complex numbers question (1 Viewer)

[ajtho777]

Hey all, I've been able to do part a but for part B I got an ans of -37 + 6sqrt(3)I . The answers in the textbook say it is -43 but I'm not sure where I went wrong.

 

[WeiWeiMan]

View attachment 43264
Hey all, I've been able to do part a but for part B I got an ans of -37 + 6sqrt(3)I . The answers in the textbook say it is -43 but I'm not sure where I went wrong.

w is a solution to z^3=-1
z^3+1=0
sum of roots =-b/a=0

-1+w-w^2=0

(6w+1)(6w^2-1)
=36w^3+6w^2-6w-1
=-36 - 6(-1+w-w^2)-6-1
= -43-0
= -43