Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((+2i) \cdot (-4+10i)= -8 i+20i^2 = \color{red}{-20}\color{blue}{-8i}\)
2. \((+4i) \cdot (-9-7i)= -36 i-28i^2 = \color{red}{28}\color{blue}{-36i}\)
3. \(\frac{-1-9i}{4+10i}= \frac{-1-9i}{4+10i} \cdot \frac{4-10i}{4-10i} = \frac{-4+10i -36 i+90i^2 }{(4)^2-(10i)^2} = \frac{-4+10i -36 i-90}{16 + 100} = \frac{-94-26i }{116} = \frac{-47}{58} + \frac{-13}{58}i \)
4. \(\frac{-4-7i}{-9-9i}= \frac{-4-7i}{-9-9i} \cdot \frac{-9+9i}{-9+9i} = \frac{36-36i +63 i-63i^2 }{(-9)^2-(-9i)^2} = \frac{36-36i +63 i+63}{81 + 81} = \frac{99+27i }{162} = \frac{11}{18} - \frac{-1}{6}i \)
5. \((-8i) \cdot (-8+3i)= +64 i-24i^2 = \color{red}{24}\color{blue}{+64i}\)
6. \(\frac{-8+9i}{7+6i}= \frac{-8+9i}{7+6i} \cdot \frac{7-6i}{7-6i} = \frac{-56+48i +63 i-54i^2 }{(7)^2-(6i)^2} = \frac{-56+48i +63 i+54}{49 + 36} = \frac{-2+111i }{85} = \frac{-2}{85} - \frac{-111}{85}i \)
7. \(\frac{5+3i}{8-8i}= \frac{5+3i}{8-8i} \cdot \frac{8+8i}{8+8i} = \frac{40+40i +24 i+24i^2 }{(8)^2-(-8i)^2} = \frac{40+40i +24 i-24}{64 + 64} = \frac{16+64i }{128} = \frac{1}{8} - \frac{-1}{2}i \)
8. \((-8-6i) \cdot (-9-4i)= 72+32i +54 i+24i^2 = 72+32i +54 i-24= \color{red}{72-24}\color{blue}{+32i +54i}=\color{red}{48}\color{blue}{+86i}\)
9. \(\frac{-10-9i}{10+7i}= \frac{-10-9i}{10+7i} \cdot \frac{10-7i}{10-7i} = \frac{-100+70i -90 i+63i^2 }{(10)^2-(7i)^2} = \frac{-100+70i -90 i-63}{100 + 49} = \frac{-163-20i }{149} = \frac{-163}{149} + \frac{-20}{149}i \)
10. \(\frac{3+9i}{9+6i}= \frac{3+9i}{9+6i} \cdot \frac{9-6i}{9-6i} = \frac{27-18i +81 i-54i^2 }{(9)^2-(6i)^2} = \frac{27-18i +81 i+54}{81 + 36} = \frac{81+63i }{117} = \frac{9}{13} - \frac{-7}{13}i \)
11. \(\frac{-3+6i}{8-9i}= \frac{-3+6i}{8-9i} \cdot \frac{8+9i}{8+9i} = \frac{-24-27i +48 i+54i^2 }{(8)^2-(-9i)^2} = \frac{-24-27i +48 i-54}{64 + 81} = \frac{-78+21i }{145} = \frac{-78}{145} - \frac{-21}{145}i \)
12. \((10-9i) \cdot (1+4i)= 10+40i -9 i-36i^2 = 10+40i -9 i+36= \color{red}{10+36}\color{blue}{+40i -9i}=\color{red}{46}\color{blue}{+31i}\)