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Eamcet Mathematics
Algebra Complex Numbers De Moivre Theorem
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Q.
If ω is a complex cube root of unity, then (x - y)(xω - y)(xω
2
- y) =
A.
x
2
+ y
2
B.
x
2
- y
2
C.
x
3
- y
3
D.
x
3
+ y
3
E.
None of the above
View Answer
Correct choice: C
Explanation:
(x -y) (xω - y) (xω
2
- y)
(x
2
ω - xy - xyω + y
2
) (xω
2
- y)
x
3
- x
2
y (1 + ω + ω
2
) +xy
2
(1 + ω + ω
2
) - y
3
= x
3
- y
3
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