Question

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

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

Answer 1

Answer: (B)

$-\sec \alpha$

$z=1+i\tan \alpha$
$\Rightarrow |z|=\sqrt{1+{\tan }^2\alpha }=\sqrt{{\sec }^2\alpha }=|\sec \alpha |$
Now we know that, modulus of any complex number is always non-zero
and it is given that, alpha lies in third quadrant in which $\sec \alpha <0$
Hence $|z|=-\sec \alpha >0$
Hence option 'B' is correct choice.