Question

Answer the question in the attachment
Class 11th​

Answer 1

-1/2 + √3/2 i = w

-1/2 - √3/2. i = w^2

And w^3 = 1

W^20 + w^2)^20 = w^20 + w^40

= w^20( 1 + w^20)

= w^18 w^2 ( 1 + w^18 w^2)

w^18 = 1

So

w^2 ( 1 + w^2)

w^2 + w^4

w^2 + w^3 w

As w^3 = 1

w^2 + w

As 1 + w + w^2 = 0

w+ w^2 = -1

So its -1

D) is correct

Answer 2

Answer:

⇒ -1/2 + √3/2 i = w

⇒ -1/2 - √3/2. i = w^2

And w^3 = 1

⇒ W^20+w^2)^20=w^20+w^40

⇒ =w^20(1+w^20)

⇒ =w^18w^2(1+w^18w^2)

⇒ w^18=1

So

⇒ w^2(1+w^2)

⇒ w^2+w^4

⇒ w^2+w^3w

⇒ Asw^3=1

⇒ w^2+w

⇒ As1+w+w^2=0

⇒ w+w^2=-1

= 1