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Manipal MET2019MathematicsComplex Number

If z₁, z₂ and z₃ are complex number such that |z₁ |= |z₂ |= |z₃ |= | 1 z₁ + 1 z₂ + 1 z₃ |=1 then |z₁+z₂+z₃ | is

Options

  1. Aequal to 1
  2. Bless than 1
  3. Cgreater than 3
  4. Dequal to 3

Correct answer

A. equal to 1

Step-by-step solution

Since, |z₁ |= |z₂ |= |z₃ |=1 we get z₁ z ₁=z₂ z ₂=z₃ z ₃=1 Now, 1= | 1 z₁ + 1 z₂ + 1 z₃ | aligned & = | z ₁+ z ₂+ z ₃ |= | z₁+z₂+z₃ | & = |z₁+z₂+z₃ | aligned

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