Question:
The point represented by \(2+i\) in the Argand plane moves 1 unit eastwards, then 2 units northwards and finally from there \(2\sqrt{2}\) units in the south-westwards direction. Then its new position in the Argand plane is at the point represented by :
The point represented by \(2+i\) in the Argand plane moves 1 unit eastwards, then 2 units northwards and finally from there \(2\sqrt{2}\) units in the south-westwards direction. Then its new position in the Argand plane is at the point represented by :
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Add each displacement as a complex number: east is +1, north is +2i, south-west is a displacement with equal negative real and imaginary parts.
Updated On: Nov 11, 2026
- \(2+2i\)
- \(1+i\)
- \(-1-i\)
- \(-2-2i\)
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The Correct Option is B
Solution and Explanation
Start: \(2+i\).
1 unit east: add \(1\): \(3+i\).
2 units north: add \(2i\): \(3+3i\).
\(2\sqrt2\) units south-west: displacement \(=2\sqrt2(\cos 225^\circ+i\sin 225^\circ)=2\sqrt2\left(-\frac{1}{\sqrt2}-\frac{i}{\sqrt2}\right)=-2-2i\).
New position: \(3+3i-2-2i=1+i\).
Answer: (2) \(1+i\)
1 unit east: add \(1\): \(3+i\).
2 units north: add \(2i\): \(3+3i\).
\(2\sqrt2\) units south-west: displacement \(=2\sqrt2(\cos 225^\circ+i\sin 225^\circ)=2\sqrt2\left(-\frac{1}{\sqrt2}-\frac{i}{\sqrt2}\right)=-2-2i\).
New position: \(3+3i-2-2i=1+i\).
Answer: (2) \(1+i\)
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