Let |z1-8-2i|≤1 and |z2-2+6i|≤2, z1, z2 ∈ C. Then the minimum value of |z1-z2| is:

Question

Let \(\left|\mathrm{z}_{1}-8-2 \mathrm{i}\right| \leq 1\) and \(\left|\mathrm{z}_{2}-2+6 \mathrm{i}\right| \leq 2,\) \(z_{1}, z_{2} \in C.\) Then the minimum value of \(\left|z_{1}-z_{2}\right|\) is:

(1) 3

(2) 7

(3) 13

(4) 10

Answer 1

Correct option is (2) 7  

\(\left|z_1-z_2\right| =C_1 C_2-\left(r_1+r_2\right) \)

\(=\sqrt{6^2+8^2}-(1+2) \)

= 10 - 3 = 7