Tabla de Números Complejos

Referencia: Leon W Couch Apéndice p653

Definiciones

$sen(x) = \frac{e^{jx}-e^{-jx}}{2j}$ $cos(x) = \frac{e^{jx}+e^{-jx}}{2}$ $tan(x) = \frac{sen(x)}{cos(x)}= \frac{e^{jx}-e^{-jx}}{j(e^{jx}+e^{-jx})}$

Teorema de Euler

$e^{\pm jx} = cos(x) \pm j sen(x)$

Complejos

$e^{\pm j\pi /2} = \pm j$ $e^{\pm jn\pi} = \begin {cases} 1 \text{, n par} \\ -1 \text{, n impar}\end{cases}$

forma rectangular

$x + jy = Re^{j\theta}$ $R = \sqrt{ x^2 + y^2}$ $\theta = tab^{-1}\left( \frac{y}{x} \right)$

a una potencia

$\left( R e^{j\theta} \right)^y = R^y e^{jy\theta}$ $\left( R_1 e^{j\theta_1} \right) \left( R_2 e^{j\theta_2} \right) = R_1 R_2 ^{j(\theta_1+\theta_2)}$