I am struggling to understand the following situation.
from the formula $$x(t) = Ae^{j\theta}cos(t)$$ find $$|x(t)|$$
the solution is $$A|cos(t)|$$
I think the reason is that you can consider each part of $x(t)$ independently, such that you have $$|Ae^{j\theta}cos(t)| = A|e^{j\theta}||cos(t)|$$
given that $|e^{j\theta}|$ is 1, the rest is not surprising. What I'm having trouble with is understanding why you can separate the product in that manner. I get that the magnitude of the product of two complex numbers is the product of their magnitudes. But I am having trouble understanding how that generalizes here. Thank you kindly for any help.