1. Initial point in Argand plane

   The complex number $2+i$ represents the point $(2,1)$ where the real part is the $x$-coordinate and the imaginary part is the $y$-coordinate.

2. Move 1 unit eastwards

   East means positive $x$-direction.

   New point: $(2,1) \to (3,1)$

3. Move 2 units northwards

   North means positive $y$-direction.

   New point: $(3,1) \to (3,3)$

4. Move $2\sqrt{2}$ units south-westwards

   South-west means equally towards south and west, i.e. along direction $(-1,-1)$.

   A displacement of magnitude $2\sqrt{2}$ in this direction has components: $\left(-\frac{1}{\sqrt{2}}\cdot 2\sqrt{2},\,-\frac{1}{\sqrt{2}}\cdot 2\sqrt{2}\right)=(-2,-2)$

   So the point becomes: $(3,3) \to (3-2,3-2)=(1,1)$

5. Convert back to complex number

   The point $(1,1)$ corresponds to $1+i$

6. Check options

   • A: $2+2i$ ❌
   • B: $1+i$ ✅
   • C: $-1-i$ ❌
   • D: $-2-2i$ ❌

Therefore, the new position is $1+i$.