EJERCICIOS RESUELTOS DE NÚMEROS COMPLEJOS

Realizar la operación indicada, escriba la respuesta de la forma a + bi.

5.- (3 + i)-(4 - 3i)

                     =3 – i – 4 + 3i

                     =-1 + 4i

6.- 2(4 - 5i)+3(-2 - i)

                              =8 – 10i – 6 - 3i

                              =2 – 3i

7.- i(-10 + 9i)- 5i

                        =-10i + 9i² + 5i

                        =-10i + 9(-1) - 5i

                        =-9 – 5i

8.- 3i(1 + i)-4(2 - i)

                            =3i + 3i² – 8 + 4i

                            =7i + 3(-1) – 8

                            =-11 +7i

9.- (3 - 2i)(2 + i)

                       =3 - 3i - 2i + 2i²

                       =3 - 5i + 2(-1)

                      =1 - 5i

10.- (7 + 14i)(2 + i)

                            =14 + 7i + 28i + 14i²

                            =14 + 35i + 14(-1)

                            =35i

11.- (4 + 5i)-(2 - i)(1 + i)

                                   =4 + 5i -(2 + 2i –i -i²)

                                   =4 + 5i-(2 + i-(-1))

                                   =4 + 5i-(3 + i)

                                   =4 + 5i – 3 - i

                                   =1 + 4i

12.-      i(1 - 2i)(2 + 5i)

=i(2 + 5i - 4i - 10i²)

=i(2 + i - 10(-1))

=i(12 + i)

=12i - i²

=-1 + 12i

13.- (5 + 6i) + (-7 + 2i)

                                 =5+6i-7+2i

                                 =-2+8i

14.- -2(6 + 4i)+5(4 - 8i)

                                  =-2 - 8i + 20 - 40i

                                  =8 - 48i

15.- i(4 + 13i) - i(1 - 9i)

                                 =4i + 13i² – i + 9i²

                                 =4i + 13(-1) –i + 9(-1)

                                 =3i – 13 - 9

                                 =-22 + 3i

16.- i + i(1 - 2i) + i(4 + 3i)

                                      =i + i - 2i² + 4i + 3i²

                                      =6i - 2(-1) + 3(-1)

                                      =-1 + 6i

17.- (4 + 6i)(-3 + 4i)

                            =-12 + 16i - 18i + 24i²

                            =-12 - 2i + 24(-1)

                            =-36-2i

18.- (2 + i)(2 - i)(1 + 3i)

                                  =(2² - i²)(1 + 3i)

                                  =(4 – (-1))(1 + 3i)

                                  =5(1 + 3i)

                                  =5 + 15i

19.- (4 + i)[(1+(1 + 3i)-2(-5 + 3i)]

                                                  =(4 + i)(i+3i²+10-6i)

                                                  =(4 + i)(i + 3(-1) + 10 - 6i)

                                                  =(4 + i)(7 – 5i)

                                                  =28 - 20i + 7i - 5i²

                                                  =28 - 13i - 5(-1)

                                                  =33 – 13i

20.- (1 + i)(1 + 2i)(1 + 3i)

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

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

                                      =(-1 + 3i)(1 + 3i)

                                      =-1 - 3i + 3i + 9i²

                                      =-1+9(-1)

                                      =-10

21.- (-3 + 6i) + (2 + 4i)(-3 + 2i)

                                              =-3 + 6i + (-6 + 4i- 12i + 8i²)

                                              =-3 + 6i – 6 - 8i + 8(-1)

                                              =-17 – 8i