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GATE 2024 Chemical Engineering, Q13 · Mathematics

The correct answer is B, π/4.

Question

If z1=−1+z₁ = −1 + i and z2=z₂ = 2i, where i =−1,= \sqrt{−1}, then Arg(z1÷z2)Arg(z₁ \div z₂) is

  • A. 3π/43π/4
  • B. π/4π/4
  • C. π/2π/2
  • D. π/3π/3

Official answer: π/4π/4

Why

GATE 2024 official key: (B). Dividing complex numbers subtracts arguments: Arg(z1÷z2)=Arg(z1)−Arg(z2).Arg(z₁ \div z₂) = Arg(z₁) − Arg(z₂). In polar form z1=−1+iz₁=−1+i is 2∠135°\sqrt{2}∠135° and z2=2iz₂=2i is 2∠90°,2∠90°, so Arg(z1/z2)=135°−90°=45°=π/4.Arg(z₁/z₂) = 135°−90° = 45° = π/4.

Explanation cross-checked for consistency. Final answer matches the official IIT answer key.

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