Q: Let ‘z’ be a complex number and ‘a’ be a real parameter such that z2 + az + a2 = 0, then
(A) locus of z is a pair of straight lines
(B) locus of z is a circle
(C) arg(z) = ± 2π/3
(D) |z| =|a|
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Ans: (A),(C) ,(D)
Sol: z2 + az + a2 = 0
⇒ z = aw, aw2 ( where ‘w’ is non real root of cube unity )
⇒ locus of z is a pair of straight lines
and arg (z) =arg(a) + arg(w) or arg(a) + arg(w2)
⇒ arg(z) = ± 2π/3
also, |z| = |a||w| or |a| |w2| ⇒ |z| = |a|
Hence (A), (C) and (D) are the correct answers.