<p>The point represented by <span>\(2+i\)</span> in the Argand plane moves 1 unit eastwards, then 2 units northwards and finally from there <span>\(2\sqrt{2}\)</span> units in the south-westwards direction. Then its new position in the Argand plane is at the point represented by</p>
Step-by-Step Solution
Key Concept: Track the complex number through sequential movements by adding displacement vectors: east is +1 on real axis, north is +i on imaginary axis, and south-west at 45° is −1−i direction scaled by distance.
<p><strong>Step 1:</strong> Initial position: z₀ = 2 + i</p><p><strong>Step 2:</strong> Move 1 unit eastwards (along positive real axis):<br/>z₁ = (2 + i) + 1 = 3 + i</p><p><strong>Step 3:</strong> Move 2 units northwards (along positive imaginary axis):<br/>z₂ = (3 + i) + 2i = 3 + 3i</p><p><strong>Step 4:</strong> Move 2√2 units south-westwards. South-west direction is at angle 225° or −135° from east, corresponding to direction vector (−1, −1)/√2. Displacement:<br/>2√2 × (−1−i)/√2 = 2√2 × (−1−i)/√2 = −2 − 2i</p><p><strong>Step 5:</strong> Final position:<br/>z₃ = (3 + 3i) + (−2 − 2i) = 1 + i</p><p>∴ Answer: A (represented by 1 + i)</p>
Correct Answer: A