Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((8+2i)\cdot (+2i)= +16 i+4i^2 = \color{red}{-4}\color{blue}{+16i}\)
2. \((-8-7i) \cdot (-4+3i)= 32-24i +28 i-21i^2 = 32-24i +28 i+21= \color{red}{32+21}\color{blue}{-24i +28i}=\color{red}{53}\color{blue}{+4i}\)
3. \((+4i) \cdot (-4-10i)= -16 i-40i^2 = \color{red}{40}\color{blue}{-16i}\)
4. \(\frac{9+4i}{10-i}= \frac{9+4i}{10-i} \cdot \frac{10+i}{10+i} = \frac{90+9i +40 i+4i^2 }{(10)^2-(-1i)^2} = \frac{90+9i +40 i-4}{100 + 1} = \frac{86+49i }{101} = \frac{86}{101} - \frac{-49}{101}i \)
5. \((-9+3i) \cdot (5-7i)= -45+63i +15 i-21i^2 = -45+63i +15 i+21= \color{red}{-45+21}\color{blue}{+63i +15i}=\color{red}{-24}\color{blue}{+78i}\)
6. \((1-5i) \cdot (8-i)= 8-i -40 i+5i^2 = 8-i -40 i-5= \color{red}{8-5}\color{blue}{-i -40i}=\color{red}{3}\color{blue}{-41i}\)
7. \((-10+5i) \cdot (1-7i)= -10+70i +5 i-35i^2 = -10+70i +5 i+35= \color{red}{-10+35}\color{blue}{+70i +5i}=\color{red}{25}\color{blue}{+75i}\)
8. \((-7-3i) \cdot (-2+i)= 14-7i +6 i-3i^2 = 14-7i +6 i+3= \color{red}{14+3}\color{blue}{-7i +6i}=\color{red}{17}\color{blue}{-i}\)
9. \(\frac{5+3i}{-2+7i}= \frac{5+3i}{-2+7i} \cdot \frac{-2-7i}{-2-7i} = \frac{-10-35i -6 i-21i^2 }{(-2)^2-(7i)^2} = \frac{-10-35i -6 i+21}{4 + 49} = \frac{11-41i }{53} = \frac{11}{53} + \frac{-41}{53}i \)
10. \((+3i) \cdot (-4+7i)= -12 i+21i^2 = \color{red}{-21}\color{blue}{-12i}\)
11. \((-2-i) \cdot (-9+2i)= 18-4i +9 i-2i^2 = 18-4i +9 i+2= \color{red}{18+2}\color{blue}{-4i +9i}=\color{red}{20}\color{blue}{+5i}\)
12. \((+i) \cdot (3-8i)= +3 i-8i^2 = \color{red}{8}\color{blue}{+3i}\)