Escribir las siguientes ecuaciones de la forma:
}&space;\right&space;\} "\mathbb{Z}=\mathbb{R}\left \{ A\\e ^{j\left ( wt+\Theta j \right )} \right \}")
1) Resolver:
-&space;2&space;\sin&space;\left&space;(&space;wt+\frac{\pi&space;}{6}&space;\right&space;) "G1= \cos \left ( wt+\frac{\pi }{4} \right )- 2 \sin \left ( wt+\frac{\pi }{6} \right )")
sabemos que:
=&space;-&space;\sin&space;\left&space;(&space;wt&space;\right&space;) "\cos \left ( wt+\frac{\pi}{2} \right )= - \sin \left ( wt \right )")
llevamos al seno a la expresión coseno
&space;+&space;2&space;\cos&space;\left&space;(&space;wt+\frac{\pi}{6}+\frac{\pi}{2}&space;\right&space;) "G1= \cos \left ( wt+\frac{\pi }{4} \right ) + 2 \cos \left ( wt+\frac{\pi}{6}+\frac{\pi}{2} \right )")
&space;+&space;2&space;\cos&space;\left&space;(&space;wt+\frac{2\pi}{3}&space;\right&space;) "G1= \cos \left ( wt+\frac{\pi }{4} \right ) + 2 \cos \left ( wt+\frac{2\pi}{3} \right )")
Ahora a la forma compleja:
Entonces:
&space;+&space;j\sin&space;\left&space;(&space;wt&space;\right&space;)\right&space;)\left&space;[&space;\cos&space;\left&space;(&space;\frac{\pi}{4}&space;\right&space;)+j\sin&space;\left&space;(&space;\frac{\pi}{4}&space;\right&space;)&space;+2\cos&space;\left&space;(&space;\frac{2\pi}{3}&space;\right&space;)+2j\sin&space;\left&space;(&space;\frac{2\pi}{3}&space;\right&space;)\right&space;] "G1=\left ( \cos \left ( wt \right ) + j\sin \left ( wt \right )\right )\left [ \cos \left ( \frac{\pi}{4} \right )+j\sin \left ( \frac{\pi}{4} \right ) +2\cos \left ( \frac{2\pi}{3} \right )+2j\sin \left ( \frac{2\pi}{3} \right )\right ]")
&space;+&space;j\sin&space;\left&space;(&space;wt&space;\right&space;)\right&space;)\left&space;[&space;\frac{\sqrt{2}}{2}+\frac{j\sqrt{2}}{2}+2\left&space;(&space;\frac{-1}{2}&space;\right&space;)+2j\left&space;(&space;\frac{\sqrt{3}}{2}&space;\right&space;)\right&space;] "G1= \left ( \cos \left ( wt \right ) + j\sin \left ( wt \right )\right )\left [ \frac{\sqrt{2}}{2}+\frac{j\sqrt{2}}{2}+2\left ( \frac{-1}{2} \right )+2j\left ( \frac{\sqrt{3}}{2} \right )\right ]")
&space;+j&space;\sin&space;\left&space;(&space;wt&space;\right&space;)\right&space;)\left&space;[&space;\frac{\sqrt{2}}{2}-1+j\left&space;(&space;\frac{\sqrt{2}}{2}&space;+&space;\sqrt{3}\right&space;)&space;\right&space;] "G1= \left ( \cos \left ( wt \right ) +j \sin \left ( wt \right )\right )\left [ \frac{\sqrt{2}}{2}-1+j\left ( \frac{\sqrt{2}}{2} + \sqrt{3}\right ) \right ]")
&space;+j\sin&space;\left&space;(&space;wt&space;\right&space;)\right&space;)\left&space;[&space;-0.29+j2.43&space;\right&space;] "G1\approx \left ( \cos \left ( wt \right ) +j\sin \left ( wt \right )\right )\left [ -0.29+j2.43 \right ]")
Para graficar solo nos interesa los valores numéricos.
Es recomendable graficar el punto
^{2}+\left&space;(&space;\frac{\sqrt{2}}{2}+\sqrt{3}&space;\right&space;)^{2}} "A=\sqrt{\left ( \frac{\sqrt{2}}{2}-1\right )^{2}+\left ( \frac{\sqrt{2}}{2}+\sqrt{3} \right )^{2}}")
 "\theta = \tanh^{-1}\left ( \frac{\mathbb{I}}{\mathbb{Re}} \right )")
 "\theta =\tan^{-1}\left ( \frac{2.43}{-0.29} \right )")
El ángulo no es principal por eso le sumamos 180 grados
Finalmente:
Nota:
&space;+&space;j\sin&space;\left&space;(&space;wt&space;\right&space;)\right&space;) "e^{jwt} = \left ( \cos \left ( wt \right ) + j\sin \left ( wt \right )\right )")
su módulo es igual a 1 y el ángulo a 0 por ende no afecta.
1) Resolver:
sabemos que:
llevamos al seno a la expresión coseno
Ahora a la forma compleja:
Entonces:
Para graficar solo nos interesa los valores numéricos.
El ángulo no es principal por eso le sumamos 180 grados
Finalmente:
Nota:
su módulo es igual a 1 y el ángulo a 0 por ende no afecta.
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