Question

Let $z_1$ and $z_2$ be two non real complex cube roots of unity and ${\left|z-z_1\right|}^2+{\left|z-z^2\right|}^2=\lambda$ be the equation of a circle with $z_1,z_2$ as ends of a diameter, then the value of $\lambda$ is

• A. 4
• B. 3
• C. 2
• D. $\sqrt{2}$

Answer 1

Answer: (B)

We have,
$|z-\omega {|}^2+{\left|z-{\omega }^2\right|}^2=\lambda$
$\Rightarrow \lambda ={\left|\omega -{\omega }^2\right|}^2=\left|{\omega }^2+{\omega }^4-2{\omega }^3\right|$
$=\left|{\omega }^2+\omega -2\right|=|-1-2|=3$