Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((+8i) \cdot (-3+4i)= -24 i+32i^2 = \color{red}{-32}\color{blue}{-24i}\)
2. \((+10i) \cdot (-2+7i)= -20 i+70i^2 = \color{red}{-70}\color{blue}{-20i}\)
3. \((10-9i) \cdot (-10+3i)= -100+30i +90 i-27i^2 = -100+30i +90 i+27= \color{red}{-100+27}\color{blue}{+30i +90i}=\color{red}{-73}\color{blue}{+120i}\)
4. \(\frac{8-i}{8+9i}= \frac{8-i}{8+9i} \cdot \frac{8-9i}{8-9i} = \frac{64-72i -8 i+9i^2 }{(8)^2-(9i)^2} = \frac{64-72i -8 i-9}{64 + 81} = \frac{55-80i }{145} = \frac{11}{29} + \frac{-16}{29}i \)
5. \((1-8i) \cdot (-7-i)= -7-i +56 i+8i^2 = -7-i +56 i-8= \color{red}{-7-8}\color{blue}{-i +56i}=\color{red}{-15}\color{blue}{+55i}\)
6. \((-9-4i) \cdot (2-8i)= -18+72i -8 i+32i^2 = -18+72i -8 i-32= \color{red}{-18-32}\color{blue}{+72i -8i}=\color{red}{-50}\color{blue}{+64i}\)
7. \((-4+i) \cdot (4+4i)= -16-16i +4 i+4i^2 = -16-16i +4 i-4= \color{red}{-16-4}\color{blue}{-16i +4i}=\color{red}{-20}\color{blue}{-12i}\)
8. \(\frac{-9-9i}{-2-10i}= \frac{-9-9i}{-2-10i} \cdot \frac{-2+10i}{-2+10i} = \frac{18-90i +18 i-90i^2 }{(-2)^2-(-10i)^2} = \frac{18-90i +18 i+90}{4 + 100} = \frac{108-72i }{104} = \frac{27}{26} + \frac{-9}{13}i \)
9. \((-1+2i) \cdot (-7-8i)= 7+8i -14 i-16i^2 = 7+8i -14 i+16= \color{red}{7+16}\color{blue}{+8i -14i}=\color{red}{23}\color{blue}{-6i}\)
10. \(\frac{8+5i}{10-2i}= \frac{8+5i}{10-2i} \cdot \frac{10+2i}{10+2i} = \frac{80+16i +50 i+10i^2 }{(10)^2-(-2i)^2} = \frac{80+16i +50 i-10}{100 + 4} = \frac{70+66i }{104} = \frac{35}{52} - \frac{-33}{52}i \)
11. \((+i) \cdot (-1+3i)= -1 i+3i^2 = \color{red}{-3}\color{blue}{-i}\)
12. \((-9+3i) \cdot (7-4i)= -63+36i +21 i-12i^2 = -63+36i +21 i+12= \color{red}{-63+12}\color{blue}{+36i +21i}=\color{red}{-51}\color{blue}{+57i}\)