Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-9-6i) \cdot (-7+3i)= 63-27i +42 i-18i^2 = 63-27i +42 i+18= \color{red}{63+18}\color{blue}{-27i +42i}=\color{red}{81}\color{blue}{+15i}\)
2. \(\frac{-7-4i}{-1+i}= \frac{-7-4i}{-1+i} \cdot \frac{-1-i}{-1-i} = \frac{7+7i +4 i+4i^2 }{(-1)^2-(1i)^2} = \frac{7+7i +4 i-4}{1 + 1} = \frac{3+11i }{2} = \frac{3}{2} - \frac{-11}{2}i \)
3. \((-1-9i)\cdot (-i)= +1 i+9i^2 = \color{red}{-9}\color{blue}{+i}\)
4. \((5-i) \cdot (3-3i)= 15-15i -3 i+3i^2 = 15-15i -3 i-3= \color{red}{15-3}\color{blue}{-15i -3i}=\color{red}{12}\color{blue}{-18i}\)
5. \((3-7i)\cdot (-3i)= -9 i+21i^2 = \color{red}{-21}\color{blue}{-9i}\)
6. \((-3i) \cdot (10-2i)= -30 i+6i^2 = \color{red}{-6}\color{blue}{-30i}\)
7. \((9-10i)\cdot (-7i)= -63 i+70i^2 = \color{red}{-70}\color{blue}{-63i}\)
8. \((-8-6i)\cdot (+5i)= -40 i-30i^2 = \color{red}{30}\color{blue}{-40i}\)
9. \((-5i) \cdot (7-10i)= -35 i+50i^2 = \color{red}{-50}\color{blue}{-35i}\)
10. \(\frac{-10+9i}{5+4i}= \frac{-10+9i}{5+4i} \cdot \frac{5-4i}{5-4i} = \frac{-50+40i +45 i-36i^2 }{(5)^2-(4i)^2} = \frac{-50+40i +45 i+36}{25 + 16} = \frac{-14+85i }{41} = \frac{-14}{41} - \frac{-85}{41}i \)
11. \(\frac{8+5i}{-1-i}= \frac{8+5i}{-1-i} \cdot \frac{-1+i}{-1+i} = \frac{-8+8i -5 i+5i^2 }{(-1)^2-(-1i)^2} = \frac{-8+8i -5 i-5}{1 + 1} = \frac{-13+3i }{2} = \frac{-13}{2} - \frac{-3}{2}i \)
12. \((-8i) \cdot (10-5i)= -80 i+40i^2 = \color{red}{-40}\color{blue}{-80i}\)