Question

1. Efetue (8 – 2i).(4 + 5i).


2. Efetue (6 + i).(6 – i).


3. Efetue (8 – i).(-1 + i).


4. Efetue (2 + 3i).(2 - 3i).


5. Sendo z = 5 – 4i, calcule z²​

Answer 1

Resposta:

1)

(8 - 2i)(4 + 5i)

8×4 + 8×5i - 2i×4 - 2i×5i

32 + 40i - 8i - 10(i^2)

32 + 32i - 10(-1)

32 + 32i + 10

42 + 32i

2)

(6 + i) (6 - i)

6×6 - 6i + 6i - i^2

36 + 0 -(-1)

36 + 1

37

3)

(8 - i) (- 1 + i)

8×(-1) + 8i + i - i^2

- 8 + 9i -(-1)

- 8 + 9i + 1

- 7 + 9i

4)

(2 + 3i)(2 - 3i)

2×2 - 6i + 6i- 9i^2

4 + 0 - 9(-1)

4 + 9

13

5)

z = 5 - 4i

z^2 = (5 - 4i)^2

z^2 = (5 - 4i)(5 - 4i)

z^2 = 5×5 - 20i - 20i + 16i^2

z^2 = 25 - 40i + 16(-1)

z^2 = 25 - 40i - 16

z^2 = 9 - 40i

Bons Estudos!