Q. If $\left| \mathcal{z} \right| = \max{\left\{ \left| \mathcal{z -}2 \right|,\ \left| \mathcal{z} + 2 \right| \right\},}\$ then
A) $\left| \mathcal{z} + \overline{\mathcal{z}} \right| = 1$
B) $\left| \mathcal{z} + \overline{\mathcal{z}} \right| = 4$
C) $\left| \mathcal{z} + \overline{\mathcal{z}} \right| = 2$
D) None of these
Explanation
(c)
If $\ \left| \mathcal{z} \right| = \left| \mathcal{z -}2 \right|\mathcal{\ \Rightarrow \ z +}\overline{\mathcal{z}} = 2$
Also, $\left| \mathcal{z} \right| = \left| \mathcal{z} + 2 \right|\mathcal{\Rightarrow \ z +}\overline{\mathcal{z}} = - 2$
Thus, $\left| \mathcal{z +}\overline{\mathcal{z}} \right| = 2$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.