Question

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

• A. $\sec \alpha$
• B. $-\sec \alpha$
• C. $cosec\alpha$
• D. None of these

Answer 1

The correct option is A $\sec \alpha$

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

then $\left|n\right|=?$ $\left|n\right|=\sqrt{1+{\tan }^2\alpha }$

$\because 1+{\tan }^2\alpha ={\sec }^2\alpha$

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

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