Output of system given input and frequency response Given the signal: $$x(t) = −4\cos(2\pi 4t) + 3\cos \left(\pi t − \frac{\pi}{3}\right)$$

By sampling theorem $Fs = 2 Maxf = 8 Hz$

The question ask what is the output of system y[n] when the signal x[n] is the input and the frequency response is: $H(e^{jω}) = 2 + 2e^{j2ω}$

I try to do this, but i don't undestand how to separate magnitude and phase from this result:
Euler's formula is you friend :) $$e^{j\theta} = \cos(\theta) + j\sin(\theta)$$
After applying it, you will have $$H(e^{j\omega}) = \Re\{H(e^{j\omega})\} + j\Im\{H(e^{j\omega})\}$$ and then it's easy to find magnitude $$|H(e^{j\omega})|=\sqrt{\Re^2\{H(e^{j\omega})\} + \Im^2\{H(e^{j\omega})\}}$$ and phase $$\angle H(e^{j\omega}) = \tan^{-1}\frac{\Im\{H(e^{j\omega})\}}{\Re\{H(e^{j\omega})\}} $$