Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-7+8i) \cdot (8-3i)= -56+21i +64 i-24i^2 = -56+21i +64 i+24= \color{red}{-56+24}\color{blue}{+21i +64i}=\color{red}{-32}\color{blue}{+85i}\)
2. \((+10i) \cdot (5-7i)= +50 i-70i^2 = \color{red}{70}\color{blue}{+50i}\)
3. \((4-7i) \cdot (6-5i)= 24-20i -42 i+35i^2 = 24-20i -42 i-35= \color{red}{24-35}\color{blue}{-20i -42i}=\color{red}{-11}\color{blue}{-62i}\)
4. \((-8+7i) \cdot (1+4i)= -8-32i +7 i+28i^2 = -8-32i +7 i-28= \color{red}{-8-28}\color{blue}{-32i +7i}=\color{red}{-36}\color{blue}{-25i}\)
5. \((-5+6i)\cdot (-7i)= +35 i-42i^2 = \color{red}{42}\color{blue}{+35i}\)
6. \(\frac{4+10i}{6+4i}= \frac{4+10i}{6+4i} \cdot \frac{6-4i}{6-4i} = \frac{24-16i +60 i-40i^2 }{(6)^2-(4i)^2} = \frac{24-16i +60 i+40}{36 + 16} = \frac{64+44i }{52} = \frac{16}{13} - \frac{-11}{13}i \)
7. \((-1+4i) \cdot (8+9i)= -8-9i +32 i+36i^2 = -8-9i +32 i-36= \color{red}{-8-36}\color{blue}{-9i +32i}=\color{red}{-44}\color{blue}{+23i}\)
8. \((7-8i) \cdot (-1-6i)= -7-42i +8 i+48i^2 = -7-42i +8 i-48= \color{red}{-7-48}\color{blue}{-42i +8i}=\color{red}{-55}\color{blue}{-34i}\)
9. \((5-5i) \cdot (10+9i)= 50+45i -50 i-45i^2 = 50+45i -50 i+45= \color{red}{50+45}\color{blue}{+45i -50i}=\color{red}{95}\color{blue}{-5i}\)
10. \(\frac{1-3i}{-8+6i}= \frac{1-3i}{-8+6i} \cdot \frac{-8-6i}{-8-6i} = \frac{-8-6i +24 i+18i^2 }{(-8)^2-(6i)^2} = \frac{-8-6i +24 i-18}{64 + 36} = \frac{-26+18i }{100} = \frac{-13}{50} - \frac{-9}{50}i \)
11. \((-2-6i) \cdot (-10+2i)= 20-4i +60 i-12i^2 = 20-4i +60 i+12= \color{red}{20+12}\color{blue}{-4i +60i}=\color{red}{32}\color{blue}{+56i}\)
12. \((1-2i)\cdot (-2i)= -2 i+4i^2 = \color{red}{-4}\color{blue}{-2i}\)