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TS EAMCET · Maths · Complex Number

If \(\left|Z_1-3-4 i\right|=5\) and \(\left|Z_2\right|=15\) then the sum of the maximum and minimum values of \(\left|Z_1-Z_2\right|\) is

  1. A 75
  2. B 30
  3. C 35
  4. D 20
Verified Solution

Answer & Solution

Correct Answer

(B) 30

Step-by-step Solution

Detailed explanation

\(c_1 = 3+4i, r_1 = 5\) \(c_2 = 0, r_2 = 15\) \(d = |c_1 - c_2| = |3+4i| = \sqrt{3^2+4^2} = 5\) \(|Z_1-Z_2|_{max} = d + r_1 + r_2 = 5 + 5 + 15 = 25\) Since \(d+r_1 \(|Z_1-Z_2|_{min} = r_2 - (d + r_1) = 15 - (5 + 5) = 5\) Sum \( = 25 + 5 = 30\)