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JEE Main2012MathematicsComplex NumberActual

|z₁+z₂ |^2+ |z₁-z₂ |^2 is equal to

Options

  1. A2 ( |z₁ |+ |z₂ | .
  2. B2 ( |z₁ |^2+ |z₂ |^2 )
  3. C|z₁ | |z₂ |
  4. D|z₁ |^2+ |z₂ |^2

Correct answer

B. 2 ( |z₁ |^2+ |z₂ |^2 )

Step-by-step solution

|z₁+z₂ |^2+ |z₁-z₂ |^2 = |z₁ |^2+ |z₂ |^2+2 |z₁ | |z₂ |+ |z₁ |^2+ |z₂ |^2-2 |z₁ | |z₂ | =2 |z₁ |^2+2 |z₂ |^2=2 [ |z₁ |^2+ |z₂ |^2 ]

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