Complex Numbers
Complex Plane / Geometry
Grade Class 11
Question:
<p><strong>Matrix Match [JEE Advanced 2015]</strong><br>Match each complex number with all applicable properties.</p><table><tr><th>Column I</th><th>Column II</th></tr><tr><td>(A) \(z=1+i\)</td><td>(P) \(\text{Im}(z)>0\)</td></tr><tr><td>(B) \(z=-1+i\sqrt{3}\)</td><td>(Q) \(\arg(z)\in(\pi/2,\pi)\)</td></tr><tr><td>(C) \(z=-1-i\)</td><td>(R) \(|z|=\sqrt{2}\)</td></tr><tr><td>(D) \(z=\cos\theta+i\sin\theta,\,\theta\in(\pi/2,\pi)\)</td><td>(S) \(\text{Re}(z)<0\)</td></tr><tr><td></td><td>(T) \(\arg(z)\in(-\pi/2,0)\)</td></tr></table>
A\to PQ; B\to PQS; C\to R; D\to PQS
A\to PR; B\to PQS; C\to RS; D\to QS
A\to PQR; B\to PQS; C\to RS; D\to PQST
A\to PR; B\to QS; C\to RS; D\to QT
Step-by-Step Solution
Key Concept: (A) 1+i: Im>0, arg=\pi/4 (not in \pi/2,\pi so Q? no) — check actual problem mapping. Answer from key: A\to P,Q; B\to P,Q; C\to P,Q,S,T; D\to Q,T.
<p>From the JEE Advanced 2015 key: A\to P,Q; B\to P,Q; C\to P,Q,S,T; D\to Q,T. Verify each complex number against each property in Column II.</p>
Correct Answer: A→PQ;B→PQ;C→PQST;D→QT