The vector represented by the complex number 2 – i is rotated about the origin through an angle

Given $2-\mathrm{i}$ is rotated by $\frac{\pi}{2}$ angle in the clockwise direction about the origin

i. e $\theta=-\frac{\pi}{2}$

Let $Z^{\prime}$ denote the new position and $Z$ denote the previous $p$

Hence $Z^{\prime}=Z e^{i \theta}=Z e^{-\frac{i \pi}{2}}$

i.e Z' $=(2-i)\left[\cos \left(\frac{-\pi}{2}\right)+1 \sin \left(\frac{-\pi}{2}\right)\right] \quad\left(\because e^{i \theta}=\cos \theta+i \sin \theta\right)$

i.e $Z^{\prime}=(2-i)[0+i(-1)]$

$=(2-i)(-i)$

$=-2 i+i^{2}$

i.e $Z^{\prime}=-1-2 i$

Hence, the correct answer is option B.