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 :
$$3$$
Solution :
$$\eqalign{ & {\left| {z - \omega } \right|^2} + {\left| {z - {\omega ^2}} \right|^2} = \lambda \cr & \Rightarrow \,\,\lambda = {\left| {\omega - {\omega ^2}} \right|^2} \cr} $$
$$\eqalign{ & {\left| {z - \omega } \right|^2} + {\left| {z - {\omega ^2}} \right|^2} = \lambda \cr & \Rightarrow \,\,\lambda = {\left| {\omega - {\omega ^2}} \right|^2} \cr} $$