Let z1 and z2 be two complex numbers satisfying | z1 | = 9 and | z2 – 3 – 4i | = 4. Then the minimum value of | z1 – z2 | is :
JEE · Math · previous-year question
- A.0correct
- B.1
- C.2
- D.$$\sqrt 2 $$
Answer
A. 0
Explanation
$$\left| {{z_1}} \right| = 9,\,\,\left| {{z_2} - \left( {3 + 4i} \right)} \right| = 4$$ $${C_1},(0,0)$$ radius r1 = 9 C2 (3, 4), radius r2 = 4 C1C2 = $$\left| {{r_1} - {r_2}} \right| = 5$$ $$ \therefore $$ Circle touches internally $$ \therefore $$ $${\left| {{z_1} - {z_2}} \right|_{\min }} = 0$$
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