Question

If $z=1+i\cot \alpha ,-\frac{\pi }{2}<\alpha <0,$ then $|z|$ is equal to

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

Answer 1

Answer: (B)

$-cosec\alpha$

$z=1+i\cot \alpha$
$\Rightarrow |z|=\sqrt{1+{\cot }^2\alpha }=\sqrt{co{\sec }^2\alpha }$
$=|co\sec \alpha |=-co\sec \alpha ,$ as $-\pi /2<\alpha <0$