Vermenigvuldigen en delen (a+bi)

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Bereken

1. \((+3i) \cdot (-6-7i)\)
2. \((2+7i)\cdot (+4i)\)
3. \((-1+2i) \cdot (-9+3i)\)
4. \((-10-2i) \cdot (10-i)\)
5. \((-6i) \cdot (3-7i)\)
6. \((+4i) \cdot (-2+8i)\)
7. \((+6i) \cdot (-4-2i)\)
8. \((-i) \cdot (-9+2i)\)
9. \((+5i) \cdot (8+3i)\)
10. \((6-5i)\cdot (+8i)\)
11. \((-4+3i)\cdot (-9i)\)
12. \(\frac{-8+6i}{8+i}\)

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Bereken

Verbetersleutel

1. \((+3i) \cdot (-6-7i)= -18 i-21i^2 = \color{red}{21}\color{blue}{-18i}\)
2. \((2+7i)\cdot (+4i)= +8 i+28i^2 = \color{red}{-28}\color{blue}{+8i}\)
3. \((-1+2i) \cdot (-9+3i)= 9-3i -18 i+6i^2 = 9-3i -18 i-6= \color{red}{9-6}\color{blue}{-3i -18i}=\color{red}{3}\color{blue}{-21i}\)
4. \((-10-2i) \cdot (10-i)= -100+10i -20 i+2i^2 = -100+10i -20 i-2= \color{red}{-100-2}\color{blue}{+10i -20i}=\color{red}{-102}\color{blue}{-10i}\)
5. \((-6i) \cdot (3-7i)= -18 i+42i^2 = \color{red}{-42}\color{blue}{-18i}\)
6. \((+4i) \cdot (-2+8i)= -8 i+32i^2 = \color{red}{-32}\color{blue}{-8i}\)
7. \((+6i) \cdot (-4-2i)= -24 i-12i^2 = \color{red}{12}\color{blue}{-24i}\)
8. \((-i) \cdot (-9+2i)= +9 i-2i^2 = \color{red}{2}\color{blue}{+9i}\)
9. \((+5i) \cdot (8+3i)= +40 i+15i^2 = \color{red}{-15}\color{blue}{+40i}\)
10. \((6-5i)\cdot (+8i)= +48 i-40i^2 = \color{red}{40}\color{blue}{+48i}\)
11. \((-4+3i)\cdot (-9i)= +36 i-27i^2 = \color{red}{27}\color{blue}{+36i}\)
12. \(\frac{-8+6i}{8+i}= \frac{-8+6i}{8+i} \cdot \frac{8-i}{8-i} = \frac{-64+8i +48 i-6i^2 }{(8)^2-(1i)^2} = \frac{-64+8i +48 i+6}{64 + 1} = \frac{-58+56i }{65} = \frac{-58}{65} - \frac{-56}{65}i \)