PrepRung
Sign inSign up free

NDA 2018 Maths · Mathematics · Complex Numbers and Quadratic Equations · medium

What is the principal argument of the complex number -1+i√3?

Single correct option

What is the principal argument of the complex number −1+i3-1+i\sqrt3?
  1. A. π3\dfrac{\pi}{3}
  2. B. −π3-\dfrac{\pi}{3}
  3. C. 2π3\dfrac{2\pi}{3}
  4. D. 5π6\dfrac{5\pi}{6}
Show answer and solution

Answer: (C) 2π3\dfrac{2\pi}{3}

The point (−1,3)(-1,\sqrt3) lies in the second quadrant. The reference angle is tan⁡−1(3/1)=π/3\tan^{-1}(\sqrt3/1)=\pi/3, so the argument is π−π/3=2π/3\pi-\pi/3=2\pi/3. The trap is π/3\pi/3, which ignores the quadrant.
Report a mistake

Original question written in the NDA 2018 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake