Solution: The expression $ \cos x + i\sin x $ corresponds to $ e^{ix} $ on the unit circle in the complex plane. Therefore, $ \cos x + i\sin x + 1 = e^{ix} + 1 $. The modulus is $ |e^{ix} + 1| $. Using the identity $ |e^{ix} + 1| = \sqrt{(\cos x + 1)^2 + \sin^2 x} $, we simplify:

Fri, 17 Apr 2026 06:08:12 +0000

Content under review