JEE Mains · Maths · STD 11 - 4.1 complex nubers
Let the circles \(C_1 : |z| = r\) and \(C_2 : |z - 3 - 4i| = 5\), \(z \in \mathbb{C}\), be such that \(C_2\) lies within \(C_1\). If \(z_1\) moves on \(C_1\), \(z_2\) moves on \(C_2\) and \(\min |z_1 - z_2| = 2\), then \(\max |z_1 - z_2|\) is equal to:
- A \(12\)
- B \(17\)
- C \(22\)
- D \(24\)
Answer & Solution
Correct Answer
(C) \(22\)
Step-by-step Solution
Detailed explanation
The center of circle \(C_1\) is \(O_1(0,0)\) and its radius is \(r_1 = r\). The center of circle \(C_2\) is \(O_2(3,4)\) and its radius is \(r_2 = 5\). The distance between the centers of the two circles is \(d = \sqrt{3^2 + 4^2} = 5\). Since \(C_2\) lies entirely within…
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