Circuit Theory/Phasors/proof5

g(t)=G_m cos(\omega t + \phi)

g(t)=G_m \operatorname{Re}(e^{j(\omega t + \phi)})

g(t)=G_{m}\operatorname {Re} (e^{j*\phi }e^{j\omega t})

g(t)=\operatorname {Re} (G_{m}e^{j*\phi }e^{j\omega t})

g(t)=\operatorname{Re}(\mathbb{G} e^{j\omega t})

\mathbb {G} =G_{m}e^{j*\phi }=G_{m}(cos(\phi )+j*sin(\phi ))=G_{m}cos(\phi )+jG_{m}sin(\phi )

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