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)}