ejercicios de numeros complejos. 4to. Bach.

Ejercicios

Representar graficamente los siguientes complejos
B = 6
D = 3 - i
E = - 5i
F = - 8 - 7i

Sumar

1) ( 4 + 2i ) + ( 2 + 3i ) =                                                            Rta: ( 6 + 5i )

2) ( -1 + i ) + ( 2 - i ) =                                                                Rta: ( 1 )

3) ( 1 - √2i ) + ( - 2 + 3√2i ) =                                                    Rta: ( - 1 - 2√2i )

4) ( 2/5 - 3i ) + ( 7/10 - 3i ) =                                                     Rta: ( 11/10 - 6i )

 

Restar

1) ( 3 + 4i ) - ( 1 + 3i ) =                                                               Rta: ( 2 - i )

2) - 1/3i - ( 1/2 - 3/5i ) =                                                                Rta: ( - 1/2 + 4/15i)

3) ( 1/5 + 3/2i ) - ( 9 - 3i ) =                                                         Rta: ( - 44/5 + 9/2i)

4) ( - 1/3 + 2/3i ) - ( 5/6 - i ) =                                                      Rta: ( - 7/6 + 5/3i )

 

Sumas algebraicas

1) ( 3/2 + 1/5i ) + ( - 1/3 + 4i ) - ( 1/2 - 1/5i ) =                                Rta: ( 2/3 + 22/5i )

2) ( 1/4i ) - ( - 5i ) - ( 3i ) = Rta: 9/4i

3) ( 5i ) + ( - 3 + 4/5i ) - ( 3/5i) - ( - 3 - 4/5i ) =                                        Rta: 6i

4) ( - 1/3i ) + ( 1/3 + 3i ) + ( -1/3 - 3i ) + ( - 5i ) =                      Rta: -16/3i

 

 

Multiplicar

1) ( 4 + 1/3i ) . ( 5 + 3/2i ) =                                                        Rta: ( 39/2 + 23/3i )

2) ( √7 - √5i ) . ( √7 + √5i ) =                                                         Rta: ( 7 - 5i )

3) ( - 1/3 - 1/2i ) . ( 2 - 4/5i ) =                                                    Rta:( - 16/15 - 11/5i )

4) ( 1/2 - i ) . ( 1/2 + i ) =                                                           Rta: - 3/4

 

Dividir

1) 3 - 3i
_______ =
- 6 + 6i
2) - 1/2 + 2i
      
___________=
2/3 - i

3) ( - 1/2 - 1/5i ) : ( - 1/2 + 1/5i ) =

4) ( - 9 - 3/5i ) : ( - 9 + 3/5i )

 

Ejercicios combinados

1) (√2 + √2 )²- ( 1 - √3i²) - √3i =
( 2 2 2 2 )

2) 1 - i - 3 =
i 2 - i
3) i ⁴ + i ⁹ + i ¹⁶
_______________ =
2 - i⁵ + i ¹⁰ - i ¹⁵
4) i¹⁸ = ( - i)⁴ = 1 = ( - i )²⁶ = ( - i )¹⁰ =
i¹⁴
a) 2i .( 1 - i ) =
b) ( - 3i )⁴ .( - 1 - i )
_________________ =
( 2i )³
Graficar y pasa a la forma polar trigonométrica
a) 4 + 4i b) -3 + i c) 5
d) - 2,5 e) 2 + 3i f) 2,5i