Let A and B be complex numbers such that AB+BA=1 .Then the origin and two points A and B from a triangle which is

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Equilateral

Obtuse angled triangle

Right angled triangle

None of these

answer is B.

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Detailed Solution

AB+BA=1⇒z2−z+1=0 ,where AB=z.So,z=ω or ω2∴AB=-ω or -ω2 so BA=-ω2 or -ω∴|AB|=1⇒|A|=|B|argAB=2π3⇒∠AOB=2π3

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