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JEE Main2014MathematicsComplex NumberActual

If z ₁, z ₂ and z ₃, z ₄ are 2 pairs of complex conjugate numbers, then ( z₁ z₄ )+ ( z₂ z₃ ) equals:

Options

  1. A0
  2. B2
  3. C3 2

Correct answer

A. 0

Step-by-step solution

Consider ( z₁ z₄ )+ ( z₂ z₃ ) = (z₁ )- (z₄ )+ (z₂ )- (z₃ ) aligned &= ( (z₁ )+ (z₂ ) )- ( (z₃ )+ (z₄ ) ) & given ( array l z₂= z ₁ z₄= z ₃ array ) &= ( (z₁ )+ ( z ₁ ) )- ( (z₃ )+ ( z ₃ ) ) & array l also ( ( z ₁ )=- (z₁ ) . ( z ₃ )=- (z₃ ) array &= ( (z₁ )- (z₁ ) )- ( (z₃ )- (z₃ ) ) &=0-0=0 aligned

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