If α,β are two complex numbers and the roots of the cubic equation (Z+α.β)3=α3,(α≠0) represent the vertices of a triangle in the Argand plane then the area of the triangle is

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334|α|2

334|α|

332|α|2

332|α|

answer is A.

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Detailed Solution

Z+αβ=α,wα,w2α Z1=α−αβZ2=wα−αβZ3=w2α−αβ|Z2−Z3|=|wα−w2α|=|w−w2||α|=3.|α|Similarly z1-z2=3α and z1-z3=3α∴area=334α2

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