Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-4i) \cdot (2-5i)= -8 i+20i^2 = \color{red}{-20}\color{blue}{-8i}\)
2. \((8+4i) \cdot (-8+10i)= -64+80i -32 i+40i^2 = -64+80i -32 i-40= \color{red}{-64-40}\color{blue}{+80i -32i}=\color{red}{-104}\color{blue}{+48i}\)
3. \((10+4i)\cdot (-10i)= -100 i-40i^2 = \color{red}{40}\color{blue}{-100i}\)
4. \((+3i) \cdot (1+10i)= +3 i+30i^2 = \color{red}{-30}\color{blue}{+3i}\)
5. \(\frac{-5-5i}{9-7i}= \frac{-5-5i}{9-7i} \cdot \frac{9+7i}{9+7i} = \frac{-45-35i -45 i-35i^2 }{(9)^2-(-7i)^2} = \frac{-45-35i -45 i+35}{81 + 49} = \frac{-10-80i }{130} = \frac{-1}{13} + \frac{-8}{13}i \)
6. \(\frac{-5-6i}{9+6i}= \frac{-5-6i}{9+6i} \cdot \frac{9-6i}{9-6i} = \frac{-45+30i -54 i+36i^2 }{(9)^2-(6i)^2} = \frac{-45+30i -54 i-36}{81 + 36} = \frac{-81-24i }{117} = \frac{-9}{13} + \frac{-8}{39}i \)
7. \((-2-i) \cdot (5+7i)= -10-14i -5 i-7i^2 = -10-14i -5 i+7= \color{red}{-10+7}\color{blue}{-14i -5i}=\color{red}{-3}\color{blue}{-19i}\)
8. \((1-3i)\cdot (+5i)= +5 i-15i^2 = \color{red}{15}\color{blue}{+5i}\)
9. \((7+4i) \cdot (-4+2i)= -28+14i -16 i+8i^2 = -28+14i -16 i-8= \color{red}{-28-8}\color{blue}{+14i -16i}=\color{red}{-36}\color{blue}{-2i}\)
10. \((9-9i) \cdot (3+7i)= 27+63i -27 i-63i^2 = 27+63i -27 i+63= \color{red}{27+63}\color{blue}{+63i -27i}=\color{red}{90}\color{blue}{+36i}\)
11. \((+9i) \cdot (7-2i)= +63 i-18i^2 = \color{red}{18}\color{blue}{+63i}\)
12. \((-2-4i) \cdot (-9-3i)= 18+6i +36 i+12i^2 = 18+6i +36 i-12= \color{red}{18-12}\color{blue}{+6i +36i}=\color{red}{6}\color{blue}{+42i}\)