Circuit Theory/Phasors/proof7


 * $$g(t)=G_m cos(\omega t - \phi)$$
 * $$g(t)=G_m \operatorname{Re}(e^{j(\omega t - \phi)})$$
 * $$g(t)=G_m \operatorname{Re}(e^{-j*\phi}e^{j\omega t})$$
 * $$g(t)=\operatorname{Re}(G_m e^{-j*\phi}e^{j\omega t})$$
 * $$g(t)=\operatorname{Re}(\mathbb{G} e^{j\omega t})$$
 * $$\mathbb{G} = G_m e^{-j*\phi} = G_m(cos(-\phi) + j*sin(-\phi)) = G_m cos(\phi) - j G_m sin(\phi)$$