NÚMEROS COMPLEJOS

GUÍA: NÚMEROS COMPLEJOS

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