Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-10+6i)\cdot (+3i)= -30 i+18i^2 = \color{red}{-18}\color{blue}{-30i}\)
2. \(\frac{-4+7i}{-3+6i}= \frac{-4+7i}{-3+6i} \cdot \frac{-3-6i}{-3-6i} = \frac{12+24i -21 i-42i^2 }{(-3)^2-(6i)^2} = \frac{12+24i -21 i+42}{9 + 36} = \frac{54+3i }{45} = \frac{6}{5} - \frac{-1}{15}i \)
3. \((6+3i)\cdot (-4i)= -24 i-12i^2 = \color{red}{12}\color{blue}{-24i}\)
4. \((5-7i)\cdot (-4i)= -20 i+28i^2 = \color{red}{-28}\color{blue}{-20i}\)
5. \((-4-4i) \cdot (-6-5i)= 24+20i +24 i+20i^2 = 24+20i +24 i-20= \color{red}{24-20}\color{blue}{+20i +24i}=\color{red}{4}\color{blue}{+44i}\)
6. \((-10-7i) \cdot (-2+8i)= 20-80i +14 i-56i^2 = 20-80i +14 i+56= \color{red}{20+56}\color{blue}{-80i +14i}=\color{red}{76}\color{blue}{-66i}\)
7. \(\frac{-1+2i}{4+6i}= \frac{-1+2i}{4+6i} \cdot \frac{4-6i}{4-6i} = \frac{-4+6i +8 i-12i^2 }{(4)^2-(6i)^2} = \frac{-4+6i +8 i+12}{16 + 36} = \frac{8+14i }{52} = \frac{2}{13} - \frac{-7}{26}i \)
8. \((4-8i) \cdot (-4+9i)= -16+36i +32 i-72i^2 = -16+36i +32 i+72= \color{red}{-16+72}\color{blue}{+36i +32i}=\color{red}{56}\color{blue}{+68i}\)
9. \((5-4i) \cdot (-10+3i)= -50+15i +40 i-12i^2 = -50+15i +40 i+12= \color{red}{-50+12}\color{blue}{+15i +40i}=\color{red}{-38}\color{blue}{+55i}\)
10. \((9+9i) \cdot (-7-10i)= -63-90i -63 i-90i^2 = -63-90i -63 i+90= \color{red}{-63+90}\color{blue}{-90i -63i}=\color{red}{27}\color{blue}{-153i}\)
11. \((-3-5i)\cdot (-4i)= +12 i+20i^2 = \color{red}{-20}\color{blue}{+12i}\)
12. \(\frac{7-10i}{2+3i}= \frac{7-10i}{2+3i} \cdot \frac{2-3i}{2-3i} = \frac{14-21i -20 i+30i^2 }{(2)^2-(3i)^2} = \frac{14-21i -20 i-30}{4 + 9} = \frac{-16-41i }{13} = \frac{-16}{13} + \frac{-41}{13}i \)