Question

1. If a and B are the complex cube roots of 1 show that,
a4 +84 +a-1.6-1 = 0.​

Answer 1

Answer:

α and β are the complex cube roots of unity.

Hence,

α=ω,β=ω

2

Since,

⇒α

4

+β

4

+α

−1

+β

−1

⇒α

4

+β

4

+

α

1

+

β

1

⇒α

4

+β

4

+

αβ

α+β

Therefore,

⇒ω

4

+(ω

2

)

4

+

ωω

2

ω+ω

2

⇒ω+ω

8

+

ω

3

−1

⇒ω+ω

2

+

1

−1

⇒−1−1

⇒−2

Hence, this is the answer.