Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-6+10i)\cdot (-2i)= +12 i-20i^2 = \color{red}{20}\color{blue}{+12i}\)
2. \((5-3i)\cdot (-i)= -5 i+3i^2 = \color{red}{-3}\color{blue}{-5i}\)
3. \(\frac{-3+6i}{-4+7i}= \frac{-3+6i}{-4+7i} \cdot \frac{-4-7i}{-4-7i} = \frac{12+21i -24 i-42i^2 }{(-4)^2-(7i)^2} = \frac{12+21i -24 i+42}{16 + 49} = \frac{54-3i }{65} = \frac{54}{65} + \frac{-3}{65}i \)
4. \((-8-8i) \cdot (2+2i)= -16-16i -16 i-16i^2 = -16-16i -16 i+16= \color{red}{-16+16}\color{blue}{-16i -16i}=\color{blue}{-32i}\)
5. \(\frac{4-9i}{2-4i}= \frac{4-9i}{2-4i} \cdot \frac{2+4i}{2+4i} = \frac{8+16i -18 i-36i^2 }{(2)^2-(-4i)^2} = \frac{8+16i -18 i+36}{4 + 16} = \frac{44-2i }{20} = \frac{11}{5} + \frac{-1}{10}i \)
6. \(\frac{-9-8i}{4-9i}= \frac{-9-8i}{4-9i} \cdot \frac{4+9i}{4+9i} = \frac{-36-81i -32 i-72i^2 }{(4)^2-(-9i)^2} = \frac{-36-81i -32 i+72}{16 + 81} = \frac{36-113i }{97} = \frac{36}{97} + \frac{-113}{97}i \)
7. \((-3+3i) \cdot (-9-8i)= 27+24i -27 i-24i^2 = 27+24i -27 i+24= \color{red}{27+24}\color{blue}{+24i -27i}=\color{red}{51}\color{blue}{-3i}\)
8. \(\frac{1-5i}{-6-8i}= \frac{1-5i}{-6-8i} \cdot \frac{-6+8i}{-6+8i} = \frac{-6+8i +30 i-40i^2 }{(-6)^2-(-8i)^2} = \frac{-6+8i +30 i+40}{36 + 64} = \frac{34+38i }{100} = \frac{17}{50} - \frac{-19}{50}i \)
9. \((-5i) \cdot (-10+4i)= +50 i-20i^2 = \color{red}{20}\color{blue}{+50i}\)
10. \((4+8i)\cdot (-9i)= -36 i-72i^2 = \color{red}{72}\color{blue}{-36i}\)
11. \(\frac{8-4i}{-5+6i}= \frac{8-4i}{-5+6i} \cdot \frac{-5-6i}{-5-6i} = \frac{-40-48i +20 i+24i^2 }{(-5)^2-(6i)^2} = \frac{-40-48i +20 i-24}{25 + 36} = \frac{-64-28i }{61} = \frac{-64}{61} + \frac{-28}{61}i \)
12. \((9+4i)\cdot (-9i)= -81 i-36i^2 = \color{red}{36}\color{blue}{-81i}\)