Question

Modulus of $\frac{cos\theta -isin\theta }{sin\theta -icos\theta }is$

• A. 0
• B. 2$\theta$
• C. $\pi -2\theta$
• D. none of these

Answer 1

Answer: (D)

none of these

$|\frac{\cos \theta -i\sin \theta }{\sin \theta -i\cos \theta }|$ $=\frac{|\cos \theta -i\sin \theta |}{|\sin \theta -i\cos \theta |}$
$=\frac{{\sin }^2\theta +{\cos }^2\theta }{{\sin }^2\theta +{\cos }^2\theta }=1$
$\therefore |\frac{\cos \theta -i\sin \theta }{\sin \theta -i\cos \theta }|=1$
Hence, option D.