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NTA Abhyas JEE Main2020MathematicsComplex NumberPractice

For a complex number Z , if Z = π 4 1 + i 4 1 - π i π + i + π - i 1 + π i , then the value of Z amp Z is equal to (where amp Z ∈ - π , π )

Options

  1. Aπ
  2. B4
  3. C1
  4. D3 π

Correct answer

B. 4

Step-by-step solution

Z = π 4 1 + i 2 2 1 - π i 1 + π i + π - i π + i π + π i + i - π ⇒ Z = π 4 1 - 1 + 2 i 2 1 + π + π + 1 π + 1 i ⇒ Z = π 4 4 - 1 2 i = - 2 π i = 2 π i ⇒ Z = 2 π and amp Z = π 2 ⇒ Z amp Z = 4

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