Question

If $x=1+i\tan \alpha$, where $\pi <\alpha <\frac{3\pi }{2}$, then $|z|$ is equal to?

Answer 1

given : $z=1+i\tan \alpha$ where, $\pi <\alpha <\frac{3\pi }{2}$

$\left|z\right|=\sqrt{1+{\tan }^2\alpha }$ $\because 1+{\tan }^2\alpha ={\sec }^2\alpha$

$\left|z\right|=\sqrt{{\sec }^2\alpha }$

$\left|z\right|=\sec \alpha$ where $\pi <\alpha <\frac{3\pi }{2}$

So option A is correct.