Complex NumbersHard
Question
If z2 + z + 1 = 0, where z is a complex number, then the value of 
is
is Options
A.18
B.54
C.6
D.12
Solution
z2 + z + 1 = 0 ⇒ Z = ω or ω2
So, z +
ω + ω2 = - 1, z2 + 
= ω2 + ω = - 1, z3 + 
= ω3 + ω3 = 2
and 
∴ The given sum = 1 + 1 + 4 + 1 + 1 + 4 = 12
So, z +
ω + ω2 = - 1, z2 + = ω2 + ω = - 1, z3 + = ω3 + ω3 = 2 and ∴ The given sum = 1 + 1 + 4 + 1 + 1 + 4 = 12
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