Complex NumbersHard
Question
If x = a + b + c, y = aα + bβ + c and z = αβ + bα + c, where α and β are imaginary cube roots of unity, then xyz =
Options
A.2(a3 + b3 + c3)
B.2(a3 - b3 - c3)
C.a3 + b3 + c3 - 3abc
D.a3 - b3 - c3
Solution
x = a + b + c
y = w(a + bw + cw2)
z = w2(a + bw2 + cw).
xyz = (a + b + c) (a + bw + cw2) (a + bw2 + cw)
= a3 + b3 + c3 - 3abc
y = w(a + bw + cw2)
z = w2(a + bw2 + cw).
xyz = (a + b + c) (a + bw + cw2) (a + bw2 + cw)
= a3 + b3 + c3 - 3abc
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