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AP EAMCET201921 Apr 2019Evening ShiftMathematicsComplex NumberActual

If a , b are the least and the greatest values respectively of z 1 + z 2 , where z 1 = 12 + 5 i and z 2 = 9 , then a 2 + b 2 =

Options

  1. A468
  2. B500
  3. C250
  4. D450

Correct answer

B. 500

Step-by-step solution

It is given that z 1 = 12 + 5 i The modulus is Z 1 = 12 2 + 5 2 ⇒ Z 1 = 144 + 25 ⇒ Z 1 = 13 The greatest value of z 1 + z 2 a = 13 + 9 ⇒ a = 22 The lowest value of z 1 + z 2 b = 13 - 9 ⇒ b = 4

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