Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \(\frac{-10+8i}{-7-5i}= \frac{-10+8i}{-7-5i} \cdot \frac{-7+5i}{-7+5i} = \frac{70-50i -56 i+40i^2 }{(-7)^2-(-5i)^2} = \frac{70-50i -56 i-40}{49 + 25} = \frac{30-106i }{74} = \frac{15}{37} + \frac{-53}{37}i \)
2. \((6+4i)\cdot (-5i)= -30 i-20i^2 = \color{red}{20}\color{blue}{-30i}\)
3. \((-7-7i)\cdot (+9i)= -63 i-63i^2 = \color{red}{63}\color{blue}{-63i}\)
4. \((+2i) \cdot (4-10i)= +8 i-20i^2 = \color{red}{20}\color{blue}{+8i}\)
5. \((2+8i) \cdot (-3+6i)= -6+12i -24 i+48i^2 = -6+12i -24 i-48= \color{red}{-6-48}\color{blue}{+12i -24i}=\color{red}{-54}\color{blue}{-12i}\)
6. \((-6+2i) \cdot (-2+8i)= 12-48i -4 i+16i^2 = 12-48i -4 i-16= \color{red}{12-16}\color{blue}{-48i -4i}=\color{red}{-4}\color{blue}{-52i}\)
7. \((1+4i)\cdot (-3i)= -3 i-12i^2 = \color{red}{12}\color{blue}{-3i}\)
8. \(\frac{8+9i}{3-6i}= \frac{8+9i}{3-6i} \cdot \frac{3+6i}{3+6i} = \frac{24+48i +27 i+54i^2 }{(3)^2-(-6i)^2} = \frac{24+48i +27 i-54}{9 + 36} = \frac{-30+75i }{45} = \frac{-2}{3} - \frac{-5}{3}i \)
9. \((8+2i)\cdot (-2i)= -16 i-4i^2 = \color{red}{4}\color{blue}{-16i}\)
10. \((2+10i)\cdot (+6i)= +12 i+60i^2 = \color{red}{-60}\color{blue}{+12i}\)
11. \((+9i) \cdot (-10-5i)= -90 i-45i^2 = \color{red}{45}\color{blue}{-90i}\)
12. \((-3i) \cdot (-5-i)= +15 i+3i^2 = \color{red}{-3}\color{blue}{+15i}\)