Question

if w is complex cube root of unity then w^50+w^51+w^52=. plz give appropriate answer then i will mark u as brainlist​

Answer 1

Answer:

ANSWER

ω is a complex cube root of unity.

⇒ω=

3

1

⇒ω

3

=1

⇒ω

3

−1=0

⇒(ω−1)(ω

2

+ω+1)=0

∴ω−1=0,ω

2

+ω+1=0 .......(1)

Consider ω

99

+ω

100

+ω

101

=ω

99

(1+ω+ω

2

)

=1

99

×0 from (1)

∴ω

99

+ω

100

+ω

101

=0