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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.

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    What needs generalizing? A, $e^{i\theta}$ and $\cos(t)$ are complex numbers. Like you say, the magnitude of their product is the product of their magnitudes. – 2017-01-10
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    `I get that the magnitude of the product of two complex numbers is the product of their magnitudes.` What's used here is that the magnitude of the product of $3$ complex numbers is the product of their magnitudes. For $z_1=A$, $z_2=e^{j\theta}$, $z_3=\cos(t)$ the last line simply says that $|z_1z_2z_3|=|z_1||z_2||z_3|\,$. – 2017-01-10
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    @dxiv ahh. makes sense now. – 2017-01-10
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    (hint to OP: abc = (ab)c ... (ab) is a complex number) – 2017-01-10

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