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(D) Rotating a complex number $z$ by $90^{\circ}$ $(+\pi/2)$ anticlockwise is equivalent to multiplying by $i$.$w_1 = z_1 	imes i = (5+4i)i = 5i + 4i

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$\pi-	an^{-1} \frac{8}{9}$

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(D) Rotating a complex number $z$ by $90^{\circ}$ $(+\pi/2)$ anticlockwise is equivalent to multiplying by $i$.$w_1 = z_1 	imes i = (5+4i)i = 5i + 4i^2 = -4+5i$.Rotating a complex number $z$ by $90^{\circ}$ $(-\pi/2)$ clockwise is equivalent to multiplying by $-i$.$w_2 = z_2 	imes (-i) = (3+5i)(-i) = -3i - 5i^2 = 5-3i$.Now,$w_1 - w_2 = (-4+5i) - (5-3i) = -9+8i$.The complex number $z = -9+8i$ lies in the second quadrant.The principal argument of $z = x+iy$ in the second quadrant is $\pi - 	an^{-1}|y/x|$.$	ext{Arg}(w_1-w_2) = \pi - 	an^{-1}\left|\frac{8}{-9}ight| = \pi - 	an^{-1}\left(\frac{8}{9}ight)$.

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