Q. If $\mathcal{z}_{1},\mathcal{z}_{2},\mathcal{z}_{3}\$ be three complex numbers such that $\left| \mathcal{z}_{1} + 1 \right| \leq 1,\left| \mathcal{z}_{2} + 2 \right| \leq 2\ and\ \left| \mathcal{z}_{3} + 4 \right| \leq 4$, then the maximum value of $\left| \mathcal{z}_{1} \right| + \left| \mathcal{z}_{2} \right| + \left| \mathcal{z}_{3} \right|$ is
A) 7
B) 10
C) 12
D) 14
Explanation
(d)
Since $\mathcal{|z +}a| \leq a$ implies $\mathcal{z}$ lies on or inside a circle with centre $( - a,\ 0)$ and radius $a,$ we have $\left| \mathcal{z}_{1} \right| + \left| \mathcal{z}_{2} \right| + \left| \mathcal{z}_{3} \right| \leq 14$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.