How to reconstruct signal of its phase and magnitude functions?
You can look at the domains covered by the Fourier transform (FT) or the DTFT (Discrete Time Fourier Transform). The DTFT applies to discrete signals, and yields a (possibly $2\pi$) periodic transformation. Here, $\omega$ denotes the continuous normalized radian frequency variable. So:

$$ (s[k])_{k\in \mathbb{Z}} \stackrel{\mathrm{DTFT}}{\longrightarrow} S(\omega) = \sum_{k=-\infty}^{\infty} s[k] z^{-k}, \quad z=e^{\imath \omega}$$
while for the FT:

$$s(t) \stackrel{\mathrm{FT}}{\longrightarrow} S(\omega) = \int_{-\infty}^{\infty} s(t) e^{- \imath \omega  t}dt$$
with no specific periodicity in general. 

So most likely, you are asked to recover a discrete signal. The complex quantity $S(\omega)$ can be recovered with  the amplitude and the phase you have. You can then recover the discrete signal using the inverse DTFT over one period:

$$s[k] =  \int_{-\pi}^{\pi} S(w)e^{\imath \omega k} d\omega \,.$$

You definitely need to check the  Discrete Time Fourier Transform (DTFT) and the associated pages.