A particle P starts from the point z_0 = 1 + | vedclass

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(D) The initial position is $z_0 = 1 + 2i$.Moving horizontally by $5$ units: $z = (1 + 5) + 2i = 6 + 2i$.Moving vertically by $3$ units: $z_1 = 6 + (2

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$-6 + 7i$

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(D) The initial position is $z_0 = 1 + 2i$.Moving horizontally by $5$ units: $z = (1 + 5) + 2i = 6 + 2i$.Moving vertically by $3$ units: $z_1 = 6 + (2 + 3)i = 6 + 5i$.From $z_1$,moving $\sqrt{2}$ units in the direction of $\hat{i} + \hat{j}$ (which is the direction of $1+i$): The unit vector is $\frac{1+i}{\sqrt{2}}$. The displacement is $\sqrt{2} 	imes \frac{1+i}{\sqrt{2}} = 1 + i$.So,the position becomes $z' = (6 + 5i) + (1 + i) = 7 + 6i$.Finally,rotating $z'$ by $\frac{\pi}{2}$ anticlockwise about the origin is equivalent to multiplying by $e^{i\pi/2} = i$.$z_2 = (7 + 6i) 	imes i = 7i + 6i^2 = 7i - 6 = -6 + 7i$.

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