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$$ \omega = \frac{2 \pi }{T} $$
$$ x(t) = A e^{j (\omega t + \phi_0)} = A \cos (\omega t + \phi_0) + j A \sin (\omega t + \phi_0) $$
$$ \cos \omega t = \frac{e^{j \omega t} + e^{-j \omega t}}{2} $$
$$ \sin \omega t = \frac{e^{j \omega t} - e^{-j \omega t}}{2j} $$