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B.1: Definición y Operaciones Básicas
https://espanol.libretexts.org/Matematicas/Calculo_Integral_CLP-2_(Feldman_Rechnitzer_y_Yeager)/04%3A_Ap%C3%A9ndices/4.02%3A_N%C3%BAmeros_Complejos_y_Exponenciales/4.2.01%3A_Definici%C3%B3n_y_Operaciones_B%C3%A1sicas
\ begin {align*} &\ left (\ frac {x} {x^2+y^2} -\ frac {y} {x^2+y^2} i\ right) (x+iy)\\ &\ hskip0.5in=\ frac {x^2} {x^2+y^2} -\ frac {xy} {x^2+y^2} i +\ frac ac {xy} {x^2+y^2} i-\ frac {y^2} {x^2+y^2}...\ begin {align*} &\ left (\ frac {x} {x^2+y^2} -\ frac {y} {x^2+y^2} i\ right) (x+iy)\\ &\ hskip0.5in=\ frac {x^2} {x^2+y^2} -\ frac {xy} {x^2+y^2} i +\ frac ac {xy} {x^2+y^2} i-\ frac {y^2} {x^2+y^2} i^2\\ &\ hskip0.5in=\ frac {x^2-i^2y^2} {x^2+y^2} =\ frac {x^2+y^2} {x^2+y^2} =1\ end {align*} $\frac{1}{z} =\frac{1}{z}\frac{\bar z}{\bar z} = \frac{\bar z}{|z|^2} =\frac{x-iy}{x^2+y^2} =\frac{x}{x^2+y^2}+\frac{-y}{x^2+y^2}i \nonumber$

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