Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((5+7i)\cdot (-9i)= -45 i-63i^2 = \color{red}{63}\color{blue}{-45i}\)
2. \((-9i) \cdot (-7+9i)= +63 i-81i^2 = \color{red}{81}\color{blue}{+63i}\)
3. \((+3i) \cdot (5+2i)= +15 i+6i^2 = \color{red}{-6}\color{blue}{+15i}\)
4. \(\frac{9-3i}{3-6i}= \frac{9-3i}{3-6i} \cdot \frac{3+6i}{3+6i} = \frac{27+54i -9 i-18i^2 }{(3)^2-(-6i)^2} = \frac{27+54i -9 i+18}{9 + 36} = \frac{45+45i }{45} = 1- -1i\)
5. \((+6i) \cdot (6+7i)= +36 i+42i^2 = \color{red}{-42}\color{blue}{+36i}\)
6. \(\frac{10-9i}{7+5i}= \frac{10-9i}{7+5i} \cdot \frac{7-5i}{7-5i} = \frac{70-50i -63 i+45i^2 }{(7)^2-(5i)^2} = \frac{70-50i -63 i-45}{49 + 25} = \frac{25-113i }{74} = \frac{25}{74} + \frac{-113}{74}i \)
7. \(\frac{-9-4i}{2-4i}= \frac{-9-4i}{2-4i} \cdot \frac{2+4i}{2+4i} = \frac{-18-36i -8 i-16i^2 }{(2)^2-(-4i)^2} = \frac{-18-36i -8 i+16}{4 + 16} = \frac{-2-44i }{20} = \frac{-1}{10} + \frac{-11}{5}i \)
8. \((5+10i) \cdot (10-2i)= 50-10i +100 i-20i^2 = 50-10i +100 i+20= \color{red}{50+20}\color{blue}{-10i +100i}=\color{red}{70}\color{blue}{+90i}\)
9. \((-i) \cdot (8-9i)= -8 i+9i^2 = \color{red}{-9}\color{blue}{-8i}\)
10. \(\frac{10+9i}{5+6i}= \frac{10+9i}{5+6i} \cdot \frac{5-6i}{5-6i} = \frac{50-60i +45 i-54i^2 }{(5)^2-(6i)^2} = \frac{50-60i +45 i+54}{25 + 36} = \frac{104-15i }{61} = \frac{104}{61} + \frac{-15}{61}i \)
11. \(\frac{-4-6i}{-9-3i}= \frac{-4-6i}{-9-3i} \cdot \frac{-9+3i}{-9+3i} = \frac{36-12i +54 i-18i^2 }{(-9)^2-(-3i)^2} = \frac{36-12i +54 i+18}{81 + 9} = \frac{54+42i }{90} = \frac{3}{5} - \frac{-7}{15}i \)
12. \((-4+2i)\cdot (+4i)= -16 i+8i^2 = \color{red}{-8}\color{blue}{-16i}\)