Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \(\frac{-9-3i}{-8+6i}= \frac{-9-3i}{-8+6i} \cdot \frac{-8-6i}{-8-6i} = \frac{72+54i +24 i+18i^2 }{(-8)^2-(6i)^2} = \frac{72+54i +24 i-18}{64 + 36} = \frac{54+78i }{100} = \frac{27}{50} - \frac{-39}{50}i \)
2. \(\frac{-10+3i}{7+8i}= \frac{-10+3i}{7+8i} \cdot \frac{7-8i}{7-8i} = \frac{-70+80i +21 i-24i^2 }{(7)^2-(8i)^2} = \frac{-70+80i +21 i+24}{49 + 64} = \frac{-46+101i }{113} = \frac{-46}{113} - \frac{-101}{113}i \)
3. \((3+7i) \cdot (-2-9i)= -6-27i -14 i-63i^2 = -6-27i -14 i+63= \color{red}{-6+63}\color{blue}{-27i -14i}=\color{red}{57}\color{blue}{-41i}\)
4. \((1+9i) \cdot (1-6i)= 1-6i +9 i-54i^2 = 1-6i +9 i+54= \color{red}{1+54}\color{blue}{-6i +9i}=\color{red}{55}\color{blue}{+3i}\)
5. \((10-10i)\cdot (-i)= -10 i+10i^2 = \color{red}{-10}\color{blue}{-10i}\)
6. \((5-i)\cdot (-7i)= -35 i+7i^2 = \color{red}{-7}\color{blue}{-35i}\)
7. \((-6+7i) \cdot (9+i)= -54-6i +63 i+7i^2 = -54-6i +63 i-7= \color{red}{-54-7}\color{blue}{-6i +63i}=\color{red}{-61}\color{blue}{+57i}\)
8. \((-5-4i)\cdot (-7i)= +35 i+28i^2 = \color{red}{-28}\color{blue}{+35i}\)
9. \((2+5i) \cdot (-10+4i)= -20+8i -50 i+20i^2 = -20+8i -50 i-20= \color{red}{-20-20}\color{blue}{+8i -50i}=\color{red}{-40}\color{blue}{-42i}\)
10. \((-8-4i) \cdot (1+10i)= -8-80i -4 i-40i^2 = -8-80i -4 i+40= \color{red}{-8+40}\color{blue}{-80i -4i}=\color{red}{32}\color{blue}{-84i}\)
11. \((4-8i) \cdot (9-6i)= 36-24i -72 i+48i^2 = 36-24i -72 i-48= \color{red}{36-48}\color{blue}{-24i -72i}=\color{red}{-12}\color{blue}{-96i}\)
12. \((7+6i)\cdot (+3i)= +21 i+18i^2 = \color{red}{-18}\color{blue}{+21i}\)