Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \(\frac{-5+8i}{-2-8i}= \frac{-5+8i}{-2-8i} \cdot \frac{-2+8i}{-2+8i} = \frac{10-40i -16 i+64i^2 }{(-2)^2-(-8i)^2} = \frac{10-40i -16 i-64}{4 + 64} = \frac{-54-56i }{68} = \frac{-27}{34} + \frac{-14}{17}i \)
2. \((-10+i) \cdot (-2+6i)= 20-60i -2 i+6i^2 = 20-60i -2 i-6= \color{red}{20-6}\color{blue}{-60i -2i}=\color{red}{14}\color{blue}{-62i}\)
3. \((-10+9i) \cdot (-6-3i)= 60+30i -54 i-27i^2 = 60+30i -54 i+27= \color{red}{60+27}\color{blue}{+30i -54i}=\color{red}{87}\color{blue}{-24i}\)
4. \((-3-9i) \cdot (-2-6i)= 6+18i +18 i+54i^2 = 6+18i +18 i-54= \color{red}{6-54}\color{blue}{+18i +18i}=\color{red}{-48}\color{blue}{+36i}\)
5. \((6+5i) \cdot (8-2i)= 48-12i +40 i-10i^2 = 48-12i +40 i+10= \color{red}{48+10}\color{blue}{-12i +40i}=\color{red}{58}\color{blue}{+28i}\)
6. \(\frac{6+3i}{3+6i}= \frac{6+3i}{3+6i} \cdot \frac{3-6i}{3-6i} = \frac{18-36i +9 i-18i^2 }{(3)^2-(6i)^2} = \frac{18-36i +9 i+18}{9 + 36} = \frac{36-27i }{45} = \frac{4}{5} + \frac{-3}{5}i \)
7. \(\frac{8-3i}{9+7i}= \frac{8-3i}{9+7i} \cdot \frac{9-7i}{9-7i} = \frac{72-56i -27 i+21i^2 }{(9)^2-(7i)^2} = \frac{72-56i -27 i-21}{81 + 49} = \frac{51-83i }{130} = \frac{51}{130} + \frac{-83}{130}i \)
8. \((-2+2i) \cdot (-7-10i)= 14+20i -14 i-20i^2 = 14+20i -14 i+20= \color{red}{14+20}\color{blue}{+20i -14i}=\color{red}{34}\color{blue}{+6i}\)
9. \((-4+8i) \cdot (1+5i)= -4-20i +8 i+40i^2 = -4-20i +8 i-40= \color{red}{-4-40}\color{blue}{-20i +8i}=\color{red}{-44}\color{blue}{-12i}\)
10. \((-10i) \cdot (8-3i)= -80 i+30i^2 = \color{red}{-30}\color{blue}{-80i}\)
11. \((+9i) \cdot (9+5i)= +81 i+45i^2 = \color{red}{-45}\color{blue}{+81i}\)
12. \((10+5i) \cdot (2+6i)= 20+60i +10 i+30i^2 = 20+60i +10 i-30= \color{red}{20-30}\color{blue}{+60i +10i}=\color{red}{-10}\color{blue}{+70i}\)