Question

# Suppose z1,z2,z3 are the vertices of an equilateral triangle inscribed in the circle |z|=2. If z1=1+i√3. 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+i√3 i.e. z2=1−√3or z3=z1ei2x/3 and z2=z1e−i2x3z3=(1+i√3)[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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