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GATE 2025 Chemical Engineering, Q13 · Mathematics

The correct answer is B, π/4.

Question

Consider two complex numbers z1=1−z₁ = 1 − i and z2=z₂ = i. The argument of z1z2z₁z₂ is

  • A. 0
  • B. π/4π/4
  • C. π/2π/2
  • D. ππ

Official answer: π/4π/4

Why

GATE 2025 official key: (B). z1z2=z₁z₂ = (1−i)(i) = i −i2=− i² = i + 1 = 1 + i, whose argument is arctan(1/1) =π/4.= π/4.

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

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