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
Create a free account to view solution
View Solution FreeMore Complex Numbers Questions
If |z1| = 2, |z2| = 3, |z3| = 4 and |2z1 + 3z2 + 4z3| = 4, then absolute value of 8z2z3 + 27z3z1 + 64z1z2 equals...If z = x + iy, then 1 ≤ | z | ≤ 3 represents-...If x2 + x + 1 = 0, then the numerical value of+.......+ is equal to...If complex number z satisfy & |arg(z - 1 - i) = , then -...The smallest positive integer n for which = 1, is...