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Highly selective Backlog Qs for JEE MainMathematicsComplex Number

If z 1 = 1 - 2 i ,   z 2 = 1 + i and z 3 = 3 + 4 i , then 1 z 1 + 2 z 2 z 3 z 2 =

Options

  1. A7 2
  2. B5 2
  3. C45 2
  4. D15 2

Correct answer

C. 45 2

Step-by-step solution

1 z 1 + 2 z 2 z 3 z 2 = 1 1 - 2 i + 2 1 + i z 3 z 2 = 1 + 2 i 1 - 2 i 1 + 2 i + 2 1 - i 1 + i 1 - i 3 2 + 4 2 1 2 + 1 2 = 1 + 2 i 5 + 2 + 2 i 2 5 2 = 5 2 1 5 + 2 i 5 + 1 - i = 1 2 6 - 3 i = 45 2

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