Class 11 - Complex Numbers
If ω be an imaginary cube root of unity, prove that (1-ω)(1-ω²)(1-ω⁵)(1-ω¹⁰)=9
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Answer:
−128ω
2
Since w is the imaginary cube root of unity
w
3
=1 and
1+w+w
2
=0 ...(i)
Hence
(1+w−w
2
)
7
=((1+w)−w
2
)
7
=(−w
2
−w
2
)
7
...from i
=(−2w
2
)
7
=−128w
14
=−128w
12
.w
2
=−128(w
3
)
4
.w
2
=−128w
2
...since w
3
=1
Step-by-step explanation:
So it help you
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