Multiplicação de números Complexos
A ) (6- i) . ( 6 – i) =
B ) (2 +3i) . (4+i) =
C) (5+7i) . ( 3- 2i) =
Soluções para a tarefa
Resposta:
a) (2 + 5i) * (1 – 2i)
2 – 4i + 5i – 10i² (lembrando que i² = – 1)
2 – 4i + 5i – 10 * (–1)
2 – 4i + 5i + 10
12 + i
b) (4 + 3i) * (2 + 6i)
8 + 24i + 6i + 18i² (lembrando que i² = – 1)
8 + 24i + 6i + 18 * (–1)
8 + 24i + 6i – 18
–10 + 30i
c) (6 – 3i) * (–3 + 7i)
–18 + 42i + 9i – 21i² (lembrando que i² = – 1)
–18 + 42i + 9i – 21 * (–1)
–18 + 42i + 9i + 21
3 + 51i
d) (10 + 10i) * (10 – 10i)
100 – 100i + 100i – 100i² (lembrando que i² = – 1)
100 – 100i + 100i – 100 * (–1)
100 + 100 + 0i
200 + 0i
200
e) 4 + 3i + (1 – 2i) * (3 + i)
4 + 3i + (3 + i – 6i – 2i²)
4 + 3i + 3 + i – 6i – 2i² (lembrando que i² = – 1)
4 + 3i + 3 + i – 6i – 2 * (–1)
4 + 3i + 3 + i – 6i + 2
9 – 2i
f) (2 – 3i) * (1 – 5i) – 4i – 8
2 – 10i – 3i + 15i² – 4i – 8 (lembrando que i² = – 1)
2 – 10i – 3i + 15 * (–1) – 4i – 8
2 – 10i – 3i – 15 – 4i – 8
2 – 15 – 8 – 10i – 3i – 4i
–21 – 17i
g) (–12 – 5i) * (5 + 5i) – 4i + 7
–60 – 60i – 25i – 25i² – 4i + 7 (lembrando que i² = – 1)
–60 – 60i – 25i – 25 * (–1) – 4i + 7
–60 – 60i – 25i + 25 – 4i + 7
–60 + 25 + 7 – 60i – 25i – 4i
–60 + 32 – 89i
–28 – 89i
h) (4 + 3i) * (2 – 5i) + (4 – 3i) * (2 + 5i)
8 – 20i + 6i – 15i² + (8 + 20i – 6i – 15i²)
8 – 20i + 6i – 15i² + 8 + 20i – 6i – 15i²
8 + 8 – 20i + 20i + 6i – 6i – 15i² – 15i²
16 – 30i² (lembrando que i² = – 1)
16 – 30 * (– 1)
46
i) (3 + 30i) * (2 – 3i) + 4 – 5i
6 – 9i + 60i – 90i² + 4 – 5i (lembrando que i² = – 1)
6 – 9i + 60i – 90 * (–1) + 4 – 5i
6 – 9i + 60i + 90 + 4 – 5i
6 + 90 + 4 – 9i + 60i – 5i
100 + 46i
j) (20 – 4i) * (2 + 5i) + (8 + 9i) * (7 – 10i) + 4 + 6i
40 + 100i – 8i – 20i² + (56 – 80i + 63i – 90i²) + 4 + 6i
40 + 100i – 8i – 20i² + 56 – 80i + 63i – 90i² + 4 + 6i (lembrando que i² = – 1)
40 + 100i – 8i – 20 * (–1) + 56 – 80i + 63i – 90 * (–1) + 4 + 6i
40 + 92i + 20 + 56 – 17i + 90 + 4 + 6i
(40 + 20 + 56 + 90 + 4) + (92i – 17i + 6i)
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