Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-3-3i)\cdot (+i)= -3 i-3i^2 = \color{red}{3}\color{blue}{-3i}\)
2. \(\frac{-3-9i}{-10-2i}= \frac{-3-9i}{-10-2i} \cdot \frac{-10+2i}{-10+2i} = \frac{30-6i +90 i-18i^2 }{(-10)^2-(-2i)^2} = \frac{30-6i +90 i+18}{100 + 4} = \frac{48+84i }{104} = \frac{6}{13} - \frac{-21}{26}i \)
3. \((3+10i)\cdot (-8i)= -24 i-80i^2 = \color{red}{80}\color{blue}{-24i}\)
4. \(\frac{-5-2i}{-1-3i}= \frac{-5-2i}{-1-3i} \cdot \frac{-1+3i}{-1+3i} = \frac{5-15i +2 i-6i^2 }{(-1)^2-(-3i)^2} = \frac{5-15i +2 i+6}{1 + 9} = \frac{11-13i }{10} = \frac{11}{10} + \frac{-13}{10}i \)
5. \((-9-7i)\cdot (+2i)= -18 i-14i^2 = \color{red}{14}\color{blue}{-18i}\)
6. \((10+5i) \cdot (9+10i)= 90+100i +45 i+50i^2 = 90+100i +45 i-50= \color{red}{90-50}\color{blue}{+100i +45i}=\color{red}{40}\color{blue}{+145i}\)
7. \((1+4i)\cdot (-7i)= -7 i-28i^2 = \color{red}{28}\color{blue}{-7i}\)
8. \((+9i) \cdot (1+3i)= +9 i+27i^2 = \color{red}{-27}\color{blue}{+9i}\)
9. \((6+i) \cdot (9-i)= 54-6i +9 i-i^2 = 54-6i +9 i+= \color{red}{54+1}\color{blue}{-6i +9i}=\color{red}{55}\color{blue}{+3i}\)
10. \(\frac{-2-2i}{9+5i}= \frac{-2-2i}{9+5i} \cdot \frac{9-5i}{9-5i} = \frac{-18+10i -18 i+10i^2 }{(9)^2-(5i)^2} = \frac{-18+10i -18 i-10}{81 + 25} = \frac{-28-8i }{106} = \frac{-14}{53} + \frac{-4}{53}i \)
11. \((-6i) \cdot (-3-8i)= +18 i+48i^2 = \color{red}{-48}\color{blue}{+18i}\)
12. \((-9+9i) \cdot (9-7i)= -81+63i +81 i-63i^2 = -81+63i +81 i+63= \color{red}{-81+63}\color{blue}{+63i +81i}=\color{red}{-18}\color{blue}{+144i}\)