Find all the roots of x^(3)-1=0. Show th...

Find all the roots of `x^(3)-1=0`. Show that if `omega` is a complex root of this equation, the other complex root is `omega^(2)` and `1+omega+omega^(2)=0.`

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Knowledge Check

If omega is an imaginary cube root of unity, then the value of (1+ omega- omega^(2))(1- omega + omega ^(2)) is-

A

1

B

2

C

4

D

8

If omega is a complex cube root of unity, then the value of (2-omega) (2-omega ^(2)) (2- omega ^(10)) (2- omega ^(11)) will be-

A

47

B

48

C

49

D

50

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