Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \(\frac{-2-10i}{-1-4i}= \frac{-2-10i}{-1-4i} \cdot \frac{-1+4i}{-1+4i} = \frac{2-8i +10 i-40i^2 }{(-1)^2-(-4i)^2} = \frac{2-8i +10 i+40}{1 + 16} = \frac{42+2i }{17} = \frac{42}{17} - \frac{-2}{17}i \)
2. \((-7i) \cdot (4-3i)= -28 i+21i^2 = \color{red}{-21}\color{blue}{-28i}\)
3. \(\frac{-8-6i}{2-8i}= \frac{-8-6i}{2-8i} \cdot \frac{2+8i}{2+8i} = \frac{-16-64i -12 i-48i^2 }{(2)^2-(-8i)^2} = \frac{-16-64i -12 i+48}{4 + 64} = \frac{32-76i }{68} = \frac{8}{17} + \frac{-19}{17}i \)
4. \((+7i) \cdot (-6+2i)= -42 i+14i^2 = \color{red}{-14}\color{blue}{-42i}\)
5. \((+4i) \cdot (2-2i)= +8 i-8i^2 = \color{red}{8}\color{blue}{+8i}\)
6. \((-5-i) \cdot (-9+2i)= 45-10i +9 i-2i^2 = 45-10i +9 i+2= \color{red}{45+2}\color{blue}{-10i +9i}=\color{red}{47}\color{blue}{-i}\)
7. \(\frac{10-4i}{-2+4i}= \frac{10-4i}{-2+4i} \cdot \frac{-2-4i}{-2-4i} = \frac{-20-40i +8 i+16i^2 }{(-2)^2-(4i)^2} = \frac{-20-40i +8 i-16}{4 + 16} = \frac{-36-32i }{20} = \frac{-9}{5} + \frac{-8}{5}i \)
8. \((3+7i) \cdot (4+2i)= 12+6i +28 i+14i^2 = 12+6i +28 i-14= \color{red}{12-14}\color{blue}{+6i +28i}=\color{red}{-2}\color{blue}{+34i}\)
9. \(\frac{-4-7i}{-2+4i}= \frac{-4-7i}{-2+4i} \cdot \frac{-2-4i}{-2-4i} = \frac{8+16i +14 i+28i^2 }{(-2)^2-(4i)^2} = \frac{8+16i +14 i-28}{4 + 16} = \frac{-20+30i }{20} = -1- \frac{-3}{2}i \)
10. \(\frac{-1+7i}{5+5i}= \frac{-1+7i}{5+5i} \cdot \frac{5-5i}{5-5i} = \frac{-5+5i +35 i-35i^2 }{(5)^2-(5i)^2} = \frac{-5+5i +35 i+35}{25 + 25} = \frac{30+40i }{50} = \frac{3}{5} - \frac{-4}{5}i \)
11. \(\frac{-10+6i}{1-10i}= \frac{-10+6i}{1-10i} \cdot \frac{1+10i}{1+10i} = \frac{-10-100i +6 i+60i^2 }{(1)^2-(-10i)^2} = \frac{-10-100i +6 i-60}{1 + 100} = \frac{-70-94i }{101} = \frac{-70}{101} + \frac{-94}{101}i \)
12. \((10-10i) \cdot (1-8i)= 10-80i -10 i+80i^2 = 10-80i -10 i-80= \color{red}{10-80}\color{blue}{-80i -10i}=\color{red}{-70}\color{blue}{-90i}\)