Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-8+4i)\cdot (+i)= -8 i+4i^2 = \color{red}{-4}\color{blue}{-8i}\)
2. \((-10+2i)\cdot (-3i)= +30 i-6i^2 = \color{red}{6}\color{blue}{+30i}\)
3. \((-6i) \cdot (8-4i)= -48 i+24i^2 = \color{red}{-24}\color{blue}{-48i}\)
4. \((-2+4i) \cdot (-2+8i)= 4-16i -8 i+32i^2 = 4-16i -8 i-32= \color{red}{4-32}\color{blue}{-16i -8i}=\color{red}{-28}\color{blue}{-24i}\)
5. \(\frac{5+8i}{-5+8i}= \frac{5+8i}{-5+8i} \cdot \frac{-5-8i}{-5-8i} = \frac{-25-40i -40 i-64i^2 }{(-5)^2-(8i)^2} = \frac{-25-40i -40 i+64}{25 + 64} = \frac{39-80i }{89} = \frac{39}{89} + \frac{-80}{89}i \)
6. \((-8+2i) \cdot (5-6i)= -40+48i +10 i-12i^2 = -40+48i +10 i+12= \color{red}{-40+12}\color{blue}{+48i +10i}=\color{red}{-28}\color{blue}{+58i}\)
7. \((-5+i) \cdot (9+7i)= -45-35i +9 i+7i^2 = -45-35i +9 i-7= \color{red}{-45-7}\color{blue}{-35i +9i}=\color{red}{-52}\color{blue}{-26i}\)
8. \((1-3i)\cdot (-i)= -1 i+3i^2 = \color{red}{-3}\color{blue}{-i}\)
9. \(\frac{2+4i}{3-6i}= \frac{2+4i}{3-6i} \cdot \frac{3+6i}{3+6i} = \frac{6+12i +12 i+24i^2 }{(3)^2-(-6i)^2} = \frac{6+12i +12 i-24}{9 + 36} = \frac{-18+24i }{45} = \frac{-2}{5} - \frac{-8}{15}i \)
10. \(\frac{6-2i}{-7-9i}= \frac{6-2i}{-7-9i} \cdot \frac{-7+9i}{-7+9i} = \frac{-42+54i +14 i-18i^2 }{(-7)^2-(-9i)^2} = \frac{-42+54i +14 i+18}{49 + 81} = \frac{-24+68i }{130} = \frac{-12}{65} - \frac{-34}{65}i \)
11. \((-9+i)\cdot (-3i)= +27 i-3i^2 = \color{red}{3}\color{blue}{+27i}\)
12. \((-3i) \cdot (10-3i)= -30 i+9i^2 = \color{red}{-9}\color{blue}{-30i}\)