1.DADOS OS NÚMEROS COMPLEXOS
Z 1 = 2 + 5 i , Z 2 = - 1 + 4 i , Z 3 = i - 2 e Z 4 = 3i
efetue :
a) Z1 + Z2 - ( Z 3 + Z 4 )
b) ( Z 1 . Z 4 ) + ( Z 2 . Z 3 )
c) ( Z 1 - Z 3 + Z 2 ² ) / Z 4
d) ( Z 1 - Z 2 . Z 4 ) / Z 3
e) ( Z 1 . Z 2 ) / Z 3 . Z 4
Respostas
Resposta:Segue as contas abaixo na explicação o que vai entender o conceito
Explicação passo-a-passo:Z 1 = 2 + 5 i , Z 2 = - 1 + 4 i , Z 3 = i - 2 e Z 4 = 3i i^2=-1
a) Z1 + Z2 - [ Z 3 + Z 4 ] b) [Z 1 . Z 4] + [ Z 2 . Z 3]
(2+5i)+(-1+4i)-[(i-2)+(3i)] [(2+5i).(3i)]+[(-1+4i).(i-2)]
2+5i-1-4i-[i-2+3i] [6i+15i^2]+[-i+2+4i^2-8i]
1+i-[4i-2] [6i+15^2]+[-9i+2+4i^2]
1+i-4i+2 [6i+15.(-1)]+[-9i+2+4.(-1)]
3-3i [6i-15]+[-9i+2-4]
[6i-15]+[-9i-2]
6i+15-9i-2
-3i+13
c) [ Z 1 - Z 3 + Z 2 ² ] / Z 4 d)[Z 1 - Z 2 . Z 4 ] / Z 3
[(2+5i)-(i-2)+(-1+4i).((-1+4i)]/3i [(2+5i)-(-1+4i).(3i)]/i-2
[2+5i-i+2+(1-4i-4i+16i^2)]/3i [(2+5i)-(-3i+12i^2)]/i-2
[4+4i+(1-8i+16i^2)]/3i [2+5i+3i-12i^2]i-2
[4+4i+1-8i+16i^2]/3i [2+8i-12i^2]/i-2
[5-4i+16.(-1)]/3i [2+8i-12.(-1)]/i-2
[5-4i-16]/3i [2+8i+12]/i-2
[-11-4i]/3i.3i/3i [14+8i]/[i-2].[i+2]/[i+2]
-33i+12i^2/9i^2 [14i+28+8i^2+16i]/[i^2+2i-2i-4]
-33i+12.(-1)/9.(-1) [30i+28+8i^2]/[i^2-4]
-33i-12/-9:3/3 [30i+28+8.(-1)]/[-1-4]
-11i-4/-3 [30i+28-8]/[-5]
30i-20/-5
-15i+4
e) Z 1 . Z 2 / Z 3 . Z 4
[2+5i).(-1+4i]/[i-2].[3i]
[-2+8i-5i+20i^2]/[3i^2-6i]
[-2+3i+20i^2]/[3i^2-6i]
[-2+3i+20.(-1)]/[3.(-1)-6i]
[-2+3i-20]/[-3-6i]
[-22+3i]/[-3-6i].[-3+6i]/[-3+6i]
[66-132i-9i+18i^2]/[9-18i+18i-36i^2]
[66-141i+18i^2]/[9-36i^2]
[66-141i+18.(-1)]/[9-36.(1)]
[66-141i-18]/[9+36]
48-141i/45:3/3
16-47i/15