Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-4+5i)\cdot (-3i)= +12 i-15i^2 = \color{red}{15}\color{blue}{+12i}\)
2. \((-2+3i)\cdot (-5i)= +10 i-15i^2 = \color{red}{15}\color{blue}{+10i}\)
3. \((-i) \cdot (2-4i)= -2 i+4i^2 = \color{red}{-4}\color{blue}{-2i}\)
4. \((2+8i) \cdot (-7+3i)= -14+6i -56 i+24i^2 = -14+6i -56 i-24= \color{red}{-14-24}\color{blue}{+6i -56i}=\color{red}{-38}\color{blue}{-50i}\)
5. \((2-8i) \cdot (3-2i)= 6-4i -24 i+16i^2 = 6-4i -24 i-16= \color{red}{6-16}\color{blue}{-4i -24i}=\color{red}{-10}\color{blue}{-28i}\)
6. \((-1-i) \cdot (-8+5i)= 8-5i +8 i-5i^2 = 8-5i +8 i+5= \color{red}{8+5}\color{blue}{-5i +8i}=\color{red}{13}\color{blue}{+3i}\)
7. \((2+6i)\cdot (+8i)= +16 i+48i^2 = \color{red}{-48}\color{blue}{+16i}\)
8. \((-2+8i)\cdot (-10i)= +20 i-80i^2 = \color{red}{80}\color{blue}{+20i}\)
9. \(\frac{-2-6i}{-7-4i}= \frac{-2-6i}{-7-4i} \cdot \frac{-7+4i}{-7+4i} = \frac{14-8i +42 i-24i^2 }{(-7)^2-(-4i)^2} = \frac{14-8i +42 i+24}{49 + 16} = \frac{38+34i }{65} = \frac{38}{65} - \frac{-34}{65}i \)
10. \((-4+3i) \cdot (-7+5i)= 28-20i -21 i+15i^2 = 28-20i -21 i-15= \color{red}{28-15}\color{blue}{-20i -21i}=\color{red}{13}\color{blue}{-41i}\)
11. \(\frac{6-4i}{3+5i}= \frac{6-4i}{3+5i} \cdot \frac{3-5i}{3-5i} = \frac{18-30i -12 i+20i^2 }{(3)^2-(5i)^2} = \frac{18-30i -12 i-20}{9 + 25} = \frac{-2-42i }{34} = \frac{-1}{17} + \frac{-21}{17}i \)
12. \((-1-7i)\cdot (+5i)= -5 i-35i^2 = \color{red}{35}\color{blue}{-5i}\)