Let z1,z2,z3 are the vertices of an equilateral triangle inscribed in the circle |z|=2 . If z1,z2,z3 are in the clockwise sense and z1=1+i3, then:

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z2=1−i3, z3=−2

z2=1−i3, z3=2

z2=1+i3, z3=−2

z2=1+i3, z3=2

answer is A.

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Detailed Solution

|z1|=|z2|=|z3|=2z1z2=z1z2e2πi/3⇒ z2=(1+i3)e−2πi/3 ⇒ z2=(1+i3)(−12−i32)⇒ z2=1−3iAlso z3z1=z1z2e2πi/3⇒ z3=(1+i3)(−12+i32)=−2

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