Question

04. If wis complex cube root of unity, then (1-w)(1 - w square)(1-wfourth root)(1 - w fifthroot
) =
a) 12
b) S
d) 15​

Answer 1

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

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