Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-1-6i)\cdot (+3i)= -3 i-18i^2 = \color{red}{18}\color{blue}{-3i}\)
2. \((4-6i) \cdot (-2-7i)= -8-28i +12 i+42i^2 = -8-28i +12 i-42= \color{red}{-8-42}\color{blue}{-28i +12i}=\color{red}{-50}\color{blue}{-16i}\)
3. \((9-4i) \cdot (-3-5i)= -27-45i +12 i+20i^2 = -27-45i +12 i-20= \color{red}{-27-20}\color{blue}{-45i +12i}=\color{red}{-47}\color{blue}{-33i}\)
4. \((-7-4i) \cdot (10+5i)= -70-35i -40 i-20i^2 = -70-35i -40 i+20= \color{red}{-70+20}\color{blue}{-35i -40i}=\color{red}{-50}\color{blue}{-75i}\)
5. \((6-8i)\cdot (-10i)= -60 i+80i^2 = \color{red}{-80}\color{blue}{-60i}\)
6. \((3-8i)\cdot (-8i)= -24 i+64i^2 = \color{red}{-64}\color{blue}{-24i}\)
7. \((10+3i) \cdot (-10+6i)= -100+60i -30 i+18i^2 = -100+60i -30 i-18= \color{red}{-100-18}\color{blue}{+60i -30i}=\color{red}{-118}\color{blue}{+30i}\)
8. \((-10-i)\cdot (-3i)= +30 i+3i^2 = \color{red}{-3}\color{blue}{+30i}\)
9. \(\frac{6+2i}{-4-6i}= \frac{6+2i}{-4-6i} \cdot \frac{-4+6i}{-4+6i} = \frac{-24+36i -8 i+12i^2 }{(-4)^2-(-6i)^2} = \frac{-24+36i -8 i-12}{16 + 36} = \frac{-36+28i }{52} = \frac{-9}{13} - \frac{-7}{13}i \)
10. \((-2i) \cdot (-6+4i)= +12 i-8i^2 = \color{red}{8}\color{blue}{+12i}\)
11. \(\frac{-7+4i}{-4-5i}= \frac{-7+4i}{-4-5i} \cdot \frac{-4+5i}{-4+5i} = \frac{28-35i -16 i+20i^2 }{(-4)^2-(-5i)^2} = \frac{28-35i -16 i-20}{16 + 25} = \frac{8-51i }{41} = \frac{8}{41} + \frac{-51}{41}i \)
12. \(\frac{1+i}{-5+10i}= \frac{1+i}{-5+10i} \cdot \frac{-5-10i}{-5-10i} = \frac{-5-10i -5 i-10i^2 }{(-5)^2-(10i)^2} = \frac{-5-10i -5 i+10}{25 + 100} = \frac{5-15i }{125} = \frac{1}{25} + \frac{-3}{25}i \)