Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-3i) \cdot (-8+4i)= +24 i-12i^2 = \color{red}{12}\color{blue}{+24i}\)
2. \(\frac{7-5i}{-3+8i}= \frac{7-5i}{-3+8i} \cdot \frac{-3-8i}{-3-8i} = \frac{-21-56i +15 i+40i^2 }{(-3)^2-(8i)^2} = \frac{-21-56i +15 i-40}{9 + 64} = \frac{-61-41i }{73} = \frac{-61}{73} + \frac{-41}{73}i \)
3. \((-4+8i)\cdot (+3i)= -12 i+24i^2 = \color{red}{-24}\color{blue}{-12i}\)
4. \((-9+5i)\cdot (+10i)= -90 i+50i^2 = \color{red}{-50}\color{blue}{-90i}\)
5. \(\frac{-10+9i}{-9-3i}= \frac{-10+9i}{-9-3i} \cdot \frac{-9+3i}{-9+3i} = \frac{90-30i -81 i+27i^2 }{(-9)^2-(-3i)^2} = \frac{90-30i -81 i-27}{81 + 9} = \frac{63-111i }{90} = \frac{7}{10} + \frac{-37}{30}i \)
6. \((-2+5i)\cdot (+10i)= -20 i+50i^2 = \color{red}{-50}\color{blue}{-20i}\)
7. \(\frac{-8-7i}{-3-7i}= \frac{-8-7i}{-3-7i} \cdot \frac{-3+7i}{-3+7i} = \frac{24-56i +21 i-49i^2 }{(-3)^2-(-7i)^2} = \frac{24-56i +21 i+49}{9 + 49} = \frac{73-35i }{58} = \frac{73}{58} + \frac{-35}{58}i \)
8. \((-4+10i)\cdot (-i)= +4 i-10i^2 = \color{red}{10}\color{blue}{+4i}\)
9. \(\frac{2-8i}{-8-5i}= \frac{2-8i}{-8-5i} \cdot \frac{-8+5i}{-8+5i} = \frac{-16+10i +64 i-40i^2 }{(-8)^2-(-5i)^2} = \frac{-16+10i +64 i+40}{64 + 25} = \frac{24+74i }{89} = \frac{24}{89} - \frac{-74}{89}i \)
10. \((8-2i) \cdot (-7-10i)= -56-80i +14 i+20i^2 = -56-80i +14 i-20= \color{red}{-56-20}\color{blue}{-80i +14i}=\color{red}{-76}\color{blue}{-66i}\)
11. \(\frac{10+6i}{-5+9i}= \frac{10+6i}{-5+9i} \cdot \frac{-5-9i}{-5-9i} = \frac{-50-90i -30 i-54i^2 }{(-5)^2-(9i)^2} = \frac{-50-90i -30 i+54}{25 + 81} = \frac{4-120i }{106} = \frac{2}{53} + \frac{-60}{53}i \)
12. \(\frac{-2-8i}{2-5i}= \frac{-2-8i}{2-5i} \cdot \frac{2+5i}{2+5i} = \frac{-4-10i -16 i-40i^2 }{(2)^2-(-5i)^2} = \frac{-4-10i -16 i+40}{4 + 25} = \frac{36-26i }{29} = \frac{36}{29} + \frac{-26}{29}i \)