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. $-2,-1+i\sqrt{3}$
• B. $-2,1-i\sqrt{3}$
• C. $-2,-1-i\sqrt{3}$
• D. $2,1-i\sqrt{3}$

Answer 1

Answer: (B)

$-2,1-i\sqrt{3}$

$z_1=1+i\sqrt{3}$

$z_1=2e^{i\pi /3}$

The other two vertices will lie along the circle rotated by an angle of $\frac{2\pi }{3}$

Hence,

$z_2=2e^{i\pi }=-2$

$z_3=2e^{5i\pi /3}=1-i\sqrt{3}$