Correct Answer - Option 1 : 1
Concept:
Modulus of complex no. z = a + ib is given by |z| = \(\rm \sqrt{a^{2}+ b^{2}}\) .
Property of complex number:
\(\rm \left|\frac {z_1}{z_2}\right| = \frac {|z_1|}{|z_2|}\)
Calculation:
Let z = \(\rm \frac {\cos 2θ - i \sin 2θ}{\cos 2θ + i \sin 2θ}\)
Taking modulus on both sides, we get
⇒ |z| = \(\rm \left|\frac {\cos 2θ - i \sin 2θ}{\cos 2θ + i \sin 2θ}\right|\)
= \(\rm \frac {|\cos 2θ - i \sin 2θ|}{|\cos 2θ + i \sin 2θ|}\)
= \(\rm \frac {\sqrt {\cos^2 2\theta + \sin^2 2\theta}}{\sqrt {\cos^2 2\theta + \sin^2 2\theta}}\)
= 1