A particle P starts from the point Z_0 = 1 + | vedclass

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(C) The initial position is $Z_0 = 1 + 2i$.Moving $5$ units horizontally away from the origin means adding $5$ to the real part: $Z_{temp} = (1 + 5) +

Vedclass · Accepted Answer

$-6 + 7i$

Vedclass · Answer

(C) The initial position is $Z_0 = 1 + 2i$.Moving $5$ units horizontally away from the origin means adding $5$ to the real part: $Z_{temp} = (1 + 5) + 2i = 6 + 2i$.Moving $3$ units vertically upwards means adding $3$ to the imaginary part: $Z_1 = 6 + (2 + 3)i = 6 + 5i$.From $Z_1$,the particle moves $\sqrt{2}$ units in the direction of $\hat{i} + \hat{j}$. The unit vector in this direction is $\frac{1}{\sqrt{2}}(\hat{i} + \hat{j}) = \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{2}}i$. Thus,the displacement is $\sqrt{2} 	imes (\frac{1}{\sqrt{2}} + \frac{1}{\sqrt{2}}i) = 1 + i$.The new position is $Z_{1.5} = (6 + 5i) + (1 + i) = 7 + 6i$.Finally,moving through an angle $\frac{\pi}{2}$ anticlockwise on a circle centered at 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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