Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((+4i) \cdot (-8-4i)= -32 i-16i^2 = \color{red}{16}\color{blue}{-32i}\)
2. \((+4i) \cdot (6+3i)= +24 i+12i^2 = \color{red}{-12}\color{blue}{+24i}\)
3. \(\frac{-8-2i}{-9+2i}= \frac{-8-2i}{-9+2i} \cdot \frac{-9-2i}{-9-2i} = \frac{72+16i +18 i+4i^2 }{(-9)^2-(2i)^2} = \frac{72+16i +18 i-4}{81 + 4} = \frac{68+34i }{85} = \frac{4}{5} - \frac{-2}{5}i \)
4. \((1+8i) \cdot (-4-4i)= -4-4i -32 i-32i^2 = -4-4i -32 i+32= \color{red}{-4+32}\color{blue}{-4i -32i}=\color{red}{28}\color{blue}{-36i}\)
5. \((8-3i) \cdot (-10+5i)= -80+40i +30 i-15i^2 = -80+40i +30 i+15= \color{red}{-80+15}\color{blue}{+40i +30i}=\color{red}{-65}\color{blue}{+70i}\)
6. \((8-7i) \cdot (4-6i)= 32-48i -28 i+42i^2 = 32-48i -28 i-42= \color{red}{32-42}\color{blue}{-48i -28i}=\color{red}{-10}\color{blue}{-76i}\)
7. \((-2-6i) \cdot (-5-i)= 10+2i +30 i+6i^2 = 10+2i +30 i-6= \color{red}{10-6}\color{blue}{+2i +30i}=\color{red}{4}\color{blue}{+32i}\)
8. \((-4+8i)\cdot (-7i)= +28 i-56i^2 = \color{red}{56}\color{blue}{+28i}\)
9. \((+2i) \cdot (8-7i)= +16 i-14i^2 = \color{red}{14}\color{blue}{+16i}\)
10. \((10+8i)\cdot (-2i)= -20 i-16i^2 = \color{red}{16}\color{blue}{-20i}\)
11. \((6-7i) \cdot (-5-9i)= -30-54i +35 i+63i^2 = -30-54i +35 i-63= \color{red}{-30-63}\color{blue}{-54i +35i}=\color{red}{-93}\color{blue}{-19i}\)
12. \((-2i) \cdot (10-10i)= -20 i+20i^2 = \color{red}{-20}\color{blue}{-20i}\)