$\large\frac{z}{|z|}=$$\cos\theta+i\sin \theta$
$arg(\large\frac{z}{|z|})=$$\theta$
$arg\big(z_1-\large\frac{z}{|z|}\big)$$-arg\big(\large\frac{z}{|z|}\big)=\frac{\pi}{2}$
$\Rightarrow arg\big(z_1-\large\frac{z}{|z|}\big)=\frac{\pi}{2}$$+\theta$
$\big|\large\frac{z}{|z|}$$-z_1\big|=3\Rightarrow \big|z_1-\large\frac{z}{|z|}\big|$$=3$
$\Rightarrow z_1-\large\frac{z}{|z|}$$=3\big[\cos(\large\frac{\pi}{2}$$+\theta)+i\sin(\large\frac{\pi}{2}$$+\theta)\big]$
$\Rightarrow z_1=\cos\theta+i\sin\theta+3[-\sin\theta+i\cos\theta]$
$\Rightarrow |z_1|=\sqrt{10}$
Hence (D) is the correct answer.