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Manipal MET2012MathematicsComplex Number

If z₁ and z₂ are two complex numbers such that |z₁ |= |z₂ |+ |z₁-z₂ | , then

Options

  1. AIm ( z₁ z₂ )=0
  2. BRe ( z₁ z₂ )=0
  3. CRe ( z₁ z₂ )= Im ( z₁ z₂ )
  4. DNone of these

Correct answer

A. Im ( z₁ z₂ )=0

Step-by-step solution

array lc & |z₁ |= |z₂ |+ |z₁-z₂ | & |z₁ |- |z₂ |= |z₁-z₂ | & ( |z₁ |- |z₂ | )^2= |z₁-z₂ |^2 & |z₁ |^2+ |z₂ |^2-2 |z₁ | |z₂ |= |z₁ |^2+ |z₂ |^2 -2 |z₁ | |z₂ | ( ₁- ₂ ) & ( ₁- ₂ )=1 & ₁- ₂=0 & (z₁ )- (z₂ )=0 & z₁ z₂ is purely real. & lm ( z₁ z₂ )=0 array

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