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6to-Actividad 9: Potencias de Números Complejos (Forma polar)-Moivre

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6to-Actividad 9: Potencias de Números Complejos (Forma polar)-Moivre

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Formas polar y De Moivre

Created by

Pablo Rafael Martinez Perez
Pablo Rafael Martinez Perez
Dominican Republic

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6to-Actividad 9: Potencias de Números Complejos (Forma polar)-Moivre
 

6to-Actividad 9: Potencias de Números Complejos (Forma polar)-MoivreOnline version

Formas polar y De Moivre

by Pablo Rafael Martinez Perez
1

La forma trigonométrica de un complejo usa:

2

El módulo representa:

3

El argumento representa:

4

En De Moivre, el exponente multiplica:

5

Si z = r(cosθ + i senθ), entonces z^2 es:

6

Multiplicar complejos en forma polar implica:

7

Dividir complejos en forma polar implica:

8

El número 5 + 5i tiene argumento:

9

El número 4 − 4i tiene argumento:

10

La fórmula de De Moivre se usa para:

Explicación

La forma trigonométrica usa cosθ + i senθ en z = r(cosθ + i sinθ).

El módulo es la magnitud del número complejo, su longitud en el plano complejo.

El argumento es el ángulo que forma el vector con el eje real.

De Moivre: (r(cosθ + i sinθ))^n = r^n (cos(nθ) + i sin(nθ)).

Le aplica la fórmula de De Moivre para n=2.

Al multiplicar, se suman los ángulos y se multiplican los módulos.

La división resta los ángulos y resta o divide los módulos.

Argumento de 5+5i está en el primer cuadrante, 45° = π/4.

En cuartos cuarto, el ángulo es -π/4.

De Moivre permite obtener potencias de números complejos en forma polar.

 
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