Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \(\frac{3-8i}{-10-2i}= \frac{3-8i}{-10-2i} \cdot \frac{-10+2i}{-10+2i} = \frac{-30+6i +80 i-16i^2 }{(-10)^2-(-2i)^2} = \frac{-30+6i +80 i+16}{100 + 4} = \frac{-14+86i }{104} = \frac{-7}{52} - \frac{-43}{52}i \)
2. \(\frac{-5+3i}{9+7i}= \frac{-5+3i}{9+7i} \cdot \frac{9-7i}{9-7i} = \frac{-45+35i +27 i-21i^2 }{(9)^2-(7i)^2} = \frac{-45+35i +27 i+21}{81 + 49} = \frac{-24+62i }{130} = \frac{-12}{65} - \frac{-31}{65}i \)
3. \((+3i) \cdot (-10-9i)= -30 i-27i^2 = \color{red}{27}\color{blue}{-30i}\)
4. \((-8-9i) \cdot (-2+5i)= 16-40i +18 i-45i^2 = 16-40i +18 i+45= \color{red}{16+45}\color{blue}{-40i +18i}=\color{red}{61}\color{blue}{-22i}\)
5. \((-5+3i)\cdot (+10i)= -50 i+30i^2 = \color{red}{-30}\color{blue}{-50i}\)
6. \(\frac{-3-2i}{-6-8i}= \frac{-3-2i}{-6-8i} \cdot \frac{-6+8i}{-6+8i} = \frac{18-24i +12 i-16i^2 }{(-6)^2-(-8i)^2} = \frac{18-24i +12 i+16}{36 + 64} = \frac{34-12i }{100} = \frac{17}{50} + \frac{-3}{25}i \)
7. \((2-4i) \cdot (5+4i)= 10+8i -20 i-16i^2 = 10+8i -20 i+16= \color{red}{10+16}\color{blue}{+8i -20i}=\color{red}{26}\color{blue}{-12i}\)
8. \((+8i) \cdot (5-8i)= +40 i-64i^2 = \color{red}{64}\color{blue}{+40i}\)
9. \((2-6i) \cdot (5-9i)= 10-18i -30 i+54i^2 = 10-18i -30 i-54= \color{red}{10-54}\color{blue}{-18i -30i}=\color{red}{-44}\color{blue}{-48i}\)
10. \((5-6i) \cdot (3-4i)= 15-20i -18 i+24i^2 = 15-20i -18 i-24= \color{red}{15-24}\color{blue}{-20i -18i}=\color{red}{-9}\color{blue}{-38i}\)
11. \(\frac{-2+9i}{7+3i}= \frac{-2+9i}{7+3i} \cdot \frac{7-3i}{7-3i} = \frac{-14+6i +63 i-27i^2 }{(7)^2-(3i)^2} = \frac{-14+6i +63 i+27}{49 + 9} = \frac{13+69i }{58} = \frac{13}{58} - \frac{-69}{58}i \)
12. \((-4+2i) \cdot (2+3i)= -8-12i +4 i+6i^2 = -8-12i +4 i-6= \color{red}{-8-6}\color{blue}{-12i +4i}=\color{red}{-14}\color{blue}{-8i}\)