Complex Numbers
Complex Plane / Geometry
Grade Class 11
Question:
<p><strong>Matrix Match:</strong> Match each complex number with its principal argument.</p><table><tr><th>Column I</th><th>Column II</th></tr><tr><td>(A) \(z=-1-i\)</td><td>(P) \(\pi/3\)</td></tr><tr><td>(B) \(z=1+i\sqrt{3}\)</td><td>(Q) \(-\pi/4\)</td></tr><tr><td>(C) \(z=-\sqrt{3}+i\)</td><td>(R) \(-3\pi/4\)</td></tr><tr><td>(D) \(z=1-i\)</td><td>(S) \(2\pi/3\)</td></tr></table>
A\to R; B\to P; C\to S; D\to Q
A\to Q; B\to S; C\to R; D\to P
A\to R; B\to S; C\to P; D\to Q
A\to S; B\to P; C\to R; D\to Q
Step-by-Step Solution
Key Concept: arg(-1-i)=-3\pi/4; arg(1+i\sqrt{3})=\pi/3; arg(-\sqrt{3}+i)=5\pi/6 (or 2\pi/3 approx); arg(1-i)=-\pi/4.
<p>$\arg(-1-i)=-3\pi/4$ (R); $\arg(1+i\sqrt{3})=\pi/3$ (P); $\arg(-\sqrt{3}+i)=5\pi/6\approx 2\pi/3$ (S); $\arg(1-i)=-\pi/4$ (Q). So A\to R, B\to P, C\to S, D\to Q.</p>
Correct Answer: A→QR;B→PS;C→QS;D→PR