Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((9+6i) \cdot (10+7i)= 90+63i +60 i+42i^2 = 90+63i +60 i-42= \color{red}{90-42}\color{blue}{+63i +60i}=\color{red}{48}\color{blue}{+123i}\)
2. \((+3i) \cdot (-8-6i)= -24 i-18i^2 = \color{red}{18}\color{blue}{-24i}\)
3. \(\frac{8+8i}{4+5i}= \frac{8+8i}{4+5i} \cdot \frac{4-5i}{4-5i} = \frac{32-40i +32 i-40i^2 }{(4)^2-(5i)^2} = \frac{32-40i +32 i+40}{16 + 25} = \frac{72-8i }{41} = \frac{72}{41} + \frac{-8}{41}i \)
4. \((3+6i)\cdot (+9i)= +27 i+54i^2 = \color{red}{-54}\color{blue}{+27i}\)
5. \((-4+4i)\cdot (+7i)= -28 i+28i^2 = \color{red}{-28}\color{blue}{-28i}\)
6. \(\frac{7+2i}{-8+10i}= \frac{7+2i}{-8+10i} \cdot \frac{-8-10i}{-8-10i} = \frac{-56-70i -16 i-20i^2 }{(-8)^2-(10i)^2} = \frac{-56-70i -16 i+20}{64 + 100} = \frac{-36-86i }{164} = \frac{-9}{41} + \frac{-43}{82}i \)
7. \((-8i) \cdot (9-6i)= -72 i+48i^2 = \color{red}{-48}\color{blue}{-72i}\)
8. \(\frac{4+7i}{1-5i}= \frac{4+7i}{1-5i} \cdot \frac{1+5i}{1+5i} = \frac{4+20i +7 i+35i^2 }{(1)^2-(-5i)^2} = \frac{4+20i +7 i-35}{1 + 25} = \frac{-31+27i }{26} = \frac{-31}{26} - \frac{-27}{26}i \)
9. \((7+4i) \cdot (6+6i)= 42+42i +24 i+24i^2 = 42+42i +24 i-24= \color{red}{42-24}\color{blue}{+42i +24i}=\color{red}{18}\color{blue}{+66i}\)
10. \(\frac{-2+i}{-1-10i}= \frac{-2+i}{-1-10i} \cdot \frac{-1+10i}{-1+10i} = \frac{2-20i -1 i+10i^2 }{(-1)^2-(-10i)^2} = \frac{2-20i -1 i-10}{1 + 100} = \frac{-8-21i }{101} = \frac{-8}{101} + \frac{-21}{101}i \)
11. \((-7-5i) \cdot (-10-i)= 70+7i +50 i+5i^2 = 70+7i +50 i-5= \color{red}{70-5}\color{blue}{+7i +50i}=\color{red}{65}\color{blue}{+57i}\)
12. \((-10+6i)\cdot (+3i)= -30 i+18i^2 = \color{red}{-18}\color{blue}{-30i}\)