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For a complex number Z , if Z - 1 + i + Z + i = 1 , then the range of the principle argument of Z is (where principle arg Z ∈ - π , π )

Options

  1. A- π 4 , π 4
  2. Bπ 4 , π 2
  3. C- π 2 , - π 4
  4. D- π 2 , π 2

Correct answer

C. - π 2 , - π 4

Step-by-step solution

Z - 1 + i + Z + i = 1 - i - - i ⇒ locus of Z is the line segment joining - i with 1 - i ⇒ minimum arg Z = - π 2 & maximum arg Z = - π 4 ⇒ principal arg Z ∈ - π 2 , - π 4

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