Questões resolvidas sobre Números Complexos e Polinômios

Números Complexos/Polinômios – Questões resolvidas.

1) Resolver a equação no campo dos complexos: +4 = 0

 = -4  ___

X = + √-4

X = + 2i

S = {-2i,2i}

 

2) Determinar o valor de k para que o número complexo z = (k+7) + 6i seja imaginário puro.

                                                                                                  k+7 = 0

                                                                                                  k = -7

 

3) Calcule:  (3 –i) + (4 + 5i) – (4 – 3i)

                          3 –i + 4 + 5i – 4 + 3i

                          3  + 4 – 4 –i + 5i+ 3i

                           3+7i

 

4) Calcule:  (3 + 2i)( 2 – 6i)

                          3.2 – 3.6i + 2i.2 – 2i.6i

                          6 – 18i + 4i – 12i²

                          6 – 14i -12(-1)

                          6 – 14i +12

                          18 – 14i = 9 – 7i

 

5) Calcule:           (8 + 2i). (2-3i) = 16 – 24i + 4i - 6 i² = 16 - 20i + 6 =  22 - 20i

                             (2+3i) . (2-3i)            4 - 9 i²             4 + 9                   13

 

       6)  Calcule i= 92   | 4     

                                 -8      23

                                 12

                                -12

         Resto =              0                          logo, i º = 1

 

      7)  Calcule:(2- 4+ x – 5) - (+ 5x – 3)

                             2- 4+ x – 5 - - 5x + 3

                             2- 5- 4x - 2

 

     8) Calcule:(2– 5) . (7 - 9x – 2)

                               5

                         14x  – 18 x⁴ – 4x³ -35x² + 45x + 10

 

    9) Determine o quociente e o resto da divisão de  P(x) = - 6+ 2+ x – 3  por   x – 2

           Utilizando Briot-Ruffini temos:

     2 |     1        -6        2        1       :    -3

        |     ↓                                      :

        |     1        -4      -6       -11      :   -25 (resto)

 

              x³ -4x² -6x – 11 (quociente)

  10) Calcule o valor numérico de P(x) = 2+ 3- x – 11                      para x = -4.

                                                  P(-4) = 2(-4) ³+ 3(-4) ²- (-4) – 11 =

                                                              2(-64) + 3(16) + 4 – 11 =

                                                                -128 + 48 – 7 =

                                                                       - 87