efetue as seguintes divisões:
A)1+2i/ 1+3i
B)2+i /4+2i
C)4+3i/4-3i
D)1-i/2+i
Soluções para a tarefa
1-3i+2i-6i^2/1-9i^2 -> 7-i/10 Real 7/10 Imaginario -i/10
B) 2+i/4+2i 2+i(4-2i)/4+2i(4-2i) -> 8-4i+4i-2i^2/16-4i^2
8+2/16+4 -> 10/20 1/2
C)4+3i/4-3i 4+3i(4+3i)/4-3i(4+3i) -> 16+12i+12i+9i^2/16-9i^2
16+24i-9/16+9 -> 7+24i/25 Real=7/25 Imaginario=24i/25
D)1-i/2+i 1-i(2-i)/2+i(2-i) -> 2-i-2i+i^2/4-i^2
1-3i/5 Real=1/5 Imaginario=-3i/5
A) 1+2i/ 1+3i = (7 - i)/10
B) 2+i /4+2i = 1/2
C) 4+3i/4-3i = (7 + 24i)/25
D) 1-i/2+i = (3 - 3i)/5
Explicação:
A) 1 + 2i = (1 + 2i).(1 - 3i) = 1 - 3i + 2i - 6i² ⇒
1 + 3i (1 + 3i).(1 - 3i) 1 - 3i + 3i - 9i²
1 - i - 6i² = 1 - i - 6(-1) = 1 - i + 6 = 7 - i
1 - 9i² 1 - 9.(-1) 1 + 9 10
B) 2 + i = (2 + i).(4 - 2i) = 8 - 4i + 4i - 2i² ⇒
4 + 2i (4 + 2i).(4 - 2i) 16 - 8u + 8i - 4i²
8 - 2i² = 8 - 2(-1) = 8 + 2 = 10 = 1
16 - 4i² 16 - 4.(-1) 16 + 4 20 2
C) 4 + 3i = (4 + 3i).(4 + 3i) = 16 + 12i + 12i + 9i² ⇒
4 - 3i (4 - 3i).(4 + 3i) 16 + 12i - 12i - 9i²
16 + 24i + 9i² = 16 + 24i + 9(-1) = 16 + 24i - 9 =
16 - 9i² 16 - 9.(-1) 16 + 9
7 + 24i
25
D) 1 - i = (1 - i).(2 - i) = 2 - i - 2i + i² ⇒
2 + i (2 + i).(2 - i) 4 - 2i + 2i - i²
2 - 3i - i² = 2 - 3i - (-1) = 2 - 3i + 1 = 3 - 3i
4 - i² 4 - (-1) 4 + 1 5
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