Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \(\frac{-9+3i}{-1+6i}= \frac{-9+3i}{-1+6i} \cdot \frac{-1-6i}{-1-6i} = \frac{9+54i -3 i-18i^2 }{(-1)^2-(6i)^2} = \frac{9+54i -3 i+18}{1 + 36} = \frac{27+51i }{37} = \frac{27}{37} - \frac{-51}{37}i \)
2. \((+9i) \cdot (2-10i)= +18 i-90i^2 = \color{red}{90}\color{blue}{+18i}\)
3. \((4+10i)\cdot (-3i)= -12 i-30i^2 = \color{red}{30}\color{blue}{-12i}\)
4. \((6+6i) \cdot (-1-8i)= -6-48i -6 i-48i^2 = -6-48i -6 i+48= \color{red}{-6+48}\color{blue}{-48i -6i}=\color{red}{42}\color{blue}{-54i}\)
5. \((4-6i)\cdot (-9i)= -36 i+54i^2 = \color{red}{-54}\color{blue}{-36i}\)
6. \(\frac{-2+i}{-1-9i}= \frac{-2+i}{-1-9i} \cdot \frac{-1+9i}{-1+9i} = \frac{2-18i -1 i+9i^2 }{(-1)^2-(-9i)^2} = \frac{2-18i -1 i-9}{1 + 81} = \frac{-7-19i }{82} = \frac{-7}{82} + \frac{-19}{82}i \)
7. \(\frac{5+6i}{5+9i}= \frac{5+6i}{5+9i} \cdot \frac{5-9i}{5-9i} = \frac{25-45i +30 i-54i^2 }{(5)^2-(9i)^2} = \frac{25-45i +30 i+54}{25 + 81} = \frac{79-15i }{106} = \frac{79}{106} + \frac{-15}{106}i \)
8. \((+5i) \cdot (-9+6i)= -45 i+30i^2 = \color{red}{-30}\color{blue}{-45i}\)
9. \((-9-6i)\cdot (+6i)= -54 i-36i^2 = \color{red}{36}\color{blue}{-54i}\)
10. \((-10i) \cdot (3+2i)= -30 i-20i^2 = \color{red}{20}\color{blue}{-30i}\)
11. \((-8i) \cdot (7-7i)= -56 i+56i^2 = \color{red}{-56}\color{blue}{-56i}\)
12. \(\frac{8-i}{-6-4i}= \frac{8-i}{-6-4i} \cdot \frac{-6+4i}{-6+4i} = \frac{-48+32i +6 i-4i^2 }{(-6)^2-(-4i)^2} = \frac{-48+32i +6 i+4}{36 + 16} = \frac{-44+38i }{52} = \frac{-11}{13} - \frac{-19}{26}i \)