Circuit Theory/Phasors/proof5


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