Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-8i) \cdot (1+7i)= -8 i-56i^2 = \color{red}{56}\color{blue}{-8i}\)
2. \((-3-10i)\cdot (-5i)= +15 i+50i^2 = \color{red}{-50}\color{blue}{+15i}\)
3. \(\frac{-4+5i}{-10-4i}= \frac{-4+5i}{-10-4i} \cdot \frac{-10+4i}{-10+4i} = \frac{40-16i -50 i+20i^2 }{(-10)^2-(-4i)^2} = \frac{40-16i -50 i-20}{100 + 16} = \frac{20-66i }{116} = \frac{5}{29} + \frac{-33}{58}i \)
4. \((-9-5i)\cdot (+8i)= -72 i-40i^2 = \color{red}{40}\color{blue}{-72i}\)
5. \(\frac{2-6i}{6-10i}= \frac{2-6i}{6-10i} \cdot \frac{6+10i}{6+10i} = \frac{12+20i -36 i-60i^2 }{(6)^2-(-10i)^2} = \frac{12+20i -36 i+60}{36 + 100} = \frac{72-16i }{136} = \frac{9}{17} + \frac{-2}{17}i \)
6. \((-3-10i) \cdot (-2+3i)= 6-9i +20 i-30i^2 = 6-9i +20 i+30= \color{red}{6+30}\color{blue}{-9i +20i}=\color{red}{36}\color{blue}{+11i}\)
7. \((-2-6i)\cdot (+6i)= -12 i-36i^2 = \color{red}{36}\color{blue}{-12i}\)
8. \((-9-7i) \cdot (-5+7i)= 45-63i +35 i-49i^2 = 45-63i +35 i+49= \color{red}{45+49}\color{blue}{-63i +35i}=\color{red}{94}\color{blue}{-28i}\)
9. \((-10i) \cdot (8-8i)= -80 i+80i^2 = \color{red}{-80}\color{blue}{-80i}\)
10. \((-5i) \cdot (-9+7i)= +45 i-35i^2 = \color{red}{35}\color{blue}{+45i}\)
11. \((-6-6i) \cdot (2+8i)= -12-48i -12 i-48i^2 = -12-48i -12 i+48= \color{red}{-12+48}\color{blue}{-48i -12i}=\color{red}{36}\color{blue}{-60i}\)
12. \(\frac{-3-6i}{2-10i}= \frac{-3-6i}{2-10i} \cdot \frac{2+10i}{2+10i} = \frac{-6-30i -12 i-60i^2 }{(2)^2-(-10i)^2} = \frac{-6-30i -12 i+60}{4 + 100} = \frac{54-42i }{104} = \frac{27}{52} + \frac{-21}{52}i \)