Question

# $$z_{1},\ z_{2},\ z_{3}$$ are vertices of equilateral triangle inscribed in the circle $$|z|=2$$ lf $$z_{1}=1+i\sqrt{3}$$ then $$z_{2}$$ and $$z_{3}$$ are?

A
2,1+i3
B
2,1i3
C
2,1i3
D
2,1i3

Solution

## The correct option is A $$-2,1-i\sqrt{3}$$$$z_1= 1+i\sqrt3$$$$z_1 = 2 e^{ i\pi /3 }$$The other two vertices will lie along the circle rotated by an angle of $$\dfrac{2\pi}{3}$$Hence, $$z_2 = 2e^{i\pi} =-2$$$$z_3 = 2e^{5i\pi/3} = 1- i\sqrt{3}$$Mathematics

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