Let z1 and z2 be two complex numbers satisfying, z1, = 9 and, z2 -- 3 -- 4i, = 4.

Question

Let z1 and z2 be two complex numbers satisfying, z1, = 9 and, z2 -- 3 -- 4i, = 4. Then the minimum value of
 z1 -- z2, is :

Accepted Answer

$$\left| {{z_1}} \right| = 9,\,\,\left| {{z_2} - \left( {3 + 4i} \right)} \right| = 4$$

${C_1},(0,0)$ radius r1 = 9

C2 (3, 4), radius r2 = 4

C1C2 = $$\left| {{r_1} - {r_2}} \right| = 5$$

$$ \therefore $$  Circle touches internally

$$ \therefore $$  $${\left| {{z_1} - {z_2}} \right|_{\min }} = 0$$

Solutions · 1