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Question

Suppose z1,z2,z3 are the vertices of an equilateral triangle inscribed in the circle |z|=2. If z1=1+i3. then values of z3 and z2 are respectively


Solution

The correct option is A
One of the number must be a conjugate of  
z1=1+i3 i.e. z2=13or z3=z1ei2x/3 and z2=z1ei2x3z3=(1+i3)[cos(2π3)+i sin2π3]=2
Aliter : Obviously |z|=2 is a circle with centre o (0, 0) and radius 2. Therefore, OA=OB=OC and this is satisfied by (a) because two vertices of any triangle cannot be same.

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