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**Hint:**In this question, we will move step by step. First move is toward the right. So, the real part of Z will get incremented. After this next move is towards the north, so the imaginary part now gets incremented. Finally we find the component of the south-east move to get the final location point.

**Complete step-by-step answer:**

Let the initial point be at A whose value is Z = 2+i

Now, point moves one unit eastward which means there will be increment in the real part of complex number Z.

$\therefore $ New position will be at B given by ${Z_1}$ = (2+1) +i = 3+i

And again the point moves 2 units northwards which means there will be an increment in the imaginary part of complex number${Z_1}$.

$\therefore $ New position will be at C given by${Z_2}$ = 3 + (2+1) i= 3+3i.

And finally it moves $2\sqrt 2 $ unit in the south-westwards direction. If we divide this move in vertical and horizontal component, then

Movement in south direction = $2\sqrt 2 \operatorname{Cos} {45^0} = 2\sqrt 2 \times \dfrac{1}{{\sqrt 2 }} = 2$.

Movement in west direction = $2\sqrt 2 \operatorname{Sin} {45^0} = 2\sqrt 2 \times \dfrac{1}{{\sqrt 2 }} = 2$ .

If we take north and east as positive then west and south move will be negative.

And the final position will be at D given by ${Z_3}$ = (3-2)+(3-2)i = 1+i.

Therefore, option C is correct.

**So, the correct answer is “Option A”.**

**Note:**Whenever we come to these types of problems always draw a figure with notify direction and remember east-west direction shows real part of complex number and north-south direction shows imaginary part of complex number.

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