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Reto de Números Complejos

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Reto de Números Complejos

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Autoevaluación sobre números complejos

Created by

Maria Elizabeth Holguin Pereyra
Maria Elizabeth Holguin Pereyra
Mexico

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Reto de Números Complejos
 

Reto de Números ComplejosOnline version

Autoevaluación sobre números complejos

by Maria Elizabeth Holguin Pereyra
1

¿Qué es un número complejo?

2

Compute: (3+2i)+(1−4i)

3

(3+2i)(1+i)=?

4

|3+4i| = ?

5

Forma polar de 3+4i, z = r(cos θ + i sin θ). El z es:

6

De Moivre: (cos 60° + i sin 60°)^3 = ?

7

La raíz principal de -4 es:

8

Solución de x^2+1=0 son:

9

Si z=a+bi y w=c+di, la suma es:

10

Conversión polar a rectangular: z=5(cos60° + i sin60°) =

Explicación

La forma a+bi usa i para representar la raíz de -1; i^2 = -1.

Se suman partes reales y partes imaginarias por separado.

(3+2i)(1+i)=3+3i+2i-2=1+5i.

Modulus es sqrt(3^2+4^2)=sqrt(25)=5.

r=√(3^2+4^2)=5; θ=arctan(4/3)≈53.13°.

(cos60+i sin60)^3 = cos180° + i sin180° = -1.

√(-4) se toma como 2i (principal).

Los ceros son i y -i, es decir ±i.

La suma de complejos se realiza por partes reales y por separado por la imaginaria.

cos60°=0.5, sin60°=√3/2≈0.866; 5(0.5)=2.5, 5(0.866)=4.33.

 
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