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Manipal MET2012MathematicsComplex Number

If | z₁ z₂ |=1 and (z₁ z₂ )=0 , then

Options

  1. Az₁=z₂
  2. B|z₂ |^2=z₁ z₂
  3. Cz₁ z₂=1
  4. DNone of these

Correct answer

B. |z₂ |^2=z₁ z₂

Step-by-step solution

Let z₁= ₁ ( ₁+i ₁ ) . Given that, | z₁ z₂ |=1 |q₁ |= |z₂ | |z₁ |= |z₂ |= ₁ Now, (z₁ z₂ )=0 (z₁ )+ (z₂ )=0 (z₂ )=- ₁ Therefore, z₂= ₁ ( (- ₁ )+i (- ₁ ) . array cc & = ₁ ( ₁-i ₁ )= z ₁ & z ₂= ( z ₁ )=z₁ z₂ z ₂=z₁ z₂ & |z₂ |^2=z₁ z₂ array

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