Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \(\frac{9-9i}{10+i}= \frac{9-9i}{10+i} \cdot \frac{10-i}{10-i} = \frac{90-9i -90 i+9i^2 }{(10)^2-(1i)^2} = \frac{90-9i -90 i-9}{100 + 1} = \frac{81-99i }{101} = \frac{81}{101} + \frac{-99}{101}i \)
2. \(\frac{-7+5i}{6+4i}= \frac{-7+5i}{6+4i} \cdot \frac{6-4i}{6-4i} = \frac{-42+28i +30 i-20i^2 }{(6)^2-(4i)^2} = \frac{-42+28i +30 i+20}{36 + 16} = \frac{-22+58i }{52} = \frac{-11}{26} - \frac{-29}{26}i \)
3. \((+6i) \cdot (-2-10i)= -12 i-60i^2 = \color{red}{60}\color{blue}{-12i}\)
4. \((-9-4i) \cdot (-9+6i)= 81-54i +36 i-24i^2 = 81-54i +36 i+24= \color{red}{81+24}\color{blue}{-54i +36i}=\color{red}{105}\color{blue}{-18i}\)
5. \((-5+9i) \cdot (-6+10i)= 30-50i -54 i+90i^2 = 30-50i -54 i-90= \color{red}{30-90}\color{blue}{-50i -54i}=\color{red}{-60}\color{blue}{-104i}\)
6. \(\frac{-5+3i}{-9+5i}= \frac{-5+3i}{-9+5i} \cdot \frac{-9-5i}{-9-5i} = \frac{45+25i -27 i-15i^2 }{(-9)^2-(5i)^2} = \frac{45+25i -27 i+15}{81 + 25} = \frac{60-2i }{106} = \frac{30}{53} + \frac{-1}{53}i \)
7. \((+7i) \cdot (2+7i)= +14 i+49i^2 = \color{red}{-49}\color{blue}{+14i}\)
8. \((1-7i) \cdot (6+5i)= 6+5i -42 i-35i^2 = 6+5i -42 i+35= \color{red}{6+35}\color{blue}{+5i -42i}=\color{red}{41}\color{blue}{-37i}\)
9. \((-10-8i)\cdot (+i)= -10 i-8i^2 = \color{red}{8}\color{blue}{-10i}\)
10. \((+3i) \cdot (6+9i)= +18 i+27i^2 = \color{red}{-27}\color{blue}{+18i}\)
11. \(\frac{-10+10i}{6+4i}= \frac{-10+10i}{6+4i} \cdot \frac{6-4i}{6-4i} = \frac{-60+40i +60 i-40i^2 }{(6)^2-(4i)^2} = \frac{-60+40i +60 i+40}{36 + 16} = \frac{-20+100i }{52} = \frac{-5}{13} - \frac{-25}{13}i \)
12. \((+3i) \cdot (-4-3i)= -12 i-9i^2 = \color{red}{9}\color{blue}{-12i}\)