Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-5+4i) \cdot (3+3i)= -15-15i +12 i+12i^2 = -15-15i +12 i-12= \color{red}{-15-12}\color{blue}{-15i +12i}=\color{red}{-27}\color{blue}{-3i}\)
2. \(\frac{8-2i}{-6-3i}= \frac{8-2i}{-6-3i} \cdot \frac{-6+3i}{-6+3i} = \frac{-48+24i +12 i-6i^2 }{(-6)^2-(-3i)^2} = \frac{-48+24i +12 i+6}{36 + 9} = \frac{-42+36i }{45} = \frac{-14}{15} - \frac{-4}{5}i \)
3. \((-8+2i) \cdot (-9+i)= 72-8i -18 i+2i^2 = 72-8i -18 i-2= \color{red}{72-2}\color{blue}{-8i -18i}=\color{red}{70}\color{blue}{-26i}\)
4. \((10-8i) \cdot (6+6i)= 60+60i -48 i-48i^2 = 60+60i -48 i+48= \color{red}{60+48}\color{blue}{+60i -48i}=\color{red}{108}\color{blue}{+12i}\)
5. \((-5-4i) \cdot (4-7i)= -20+35i -16 i+28i^2 = -20+35i -16 i-28= \color{red}{-20-28}\color{blue}{+35i -16i}=\color{red}{-48}\color{blue}{+19i}\)
6. \(\frac{10+6i}{-6-8i}= \frac{10+6i}{-6-8i} \cdot \frac{-6+8i}{-6+8i} = \frac{-60+80i -36 i+48i^2 }{(-6)^2-(-8i)^2} = \frac{-60+80i -36 i-48}{36 + 64} = \frac{-108+44i }{100} = \frac{-27}{25} - \frac{-11}{25}i \)
7. \(\frac{9+8i}{9-4i}= \frac{9+8i}{9-4i} \cdot \frac{9+4i}{9+4i} = \frac{81+36i +72 i+32i^2 }{(9)^2-(-4i)^2} = \frac{81+36i +72 i-32}{81 + 16} = \frac{49+108i }{97} = \frac{49}{97} - \frac{-108}{97}i \)
8. \((-6-2i) \cdot (7-10i)= -42+60i -14 i+20i^2 = -42+60i -14 i-20= \color{red}{-42-20}\color{blue}{+60i -14i}=\color{red}{-62}\color{blue}{+46i}\)
9. \((-5-7i) \cdot (3+i)= -15-5i -21 i-7i^2 = -15-5i -21 i+7= \color{red}{-15+7}\color{blue}{-5i -21i}=\color{red}{-8}\color{blue}{-26i}\)
10. \(\frac{-2-6i}{10+7i}= \frac{-2-6i}{10+7i} \cdot \frac{10-7i}{10-7i} = \frac{-20+14i -60 i+42i^2 }{(10)^2-(7i)^2} = \frac{-20+14i -60 i-42}{100 + 49} = \frac{-62-46i }{149} = \frac{-62}{149} + \frac{-46}{149}i \)
11. \((-7+10i)\cdot (-i)= +7 i-10i^2 = \color{red}{10}\color{blue}{+7i}\)
12. \((-1-6i) \cdot (-4-4i)= 4+4i +24 i+24i^2 = 4+4i +24 i-24= \color{red}{4-24}\color{blue}{+4i +24i}=\color{red}{-20}\color{blue}{+28i}\)