Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((+2i) \cdot (5-5i)= +10 i-10i^2 = \color{red}{10}\color{blue}{+10i}\)
2. \(\frac{5-i}{-6-3i}= \frac{5-i}{-6-3i} \cdot \frac{-6+3i}{-6+3i} = \frac{-30+15i +6 i-3i^2 }{(-6)^2-(-3i)^2} = \frac{-30+15i +6 i+3}{36 + 9} = \frac{-27+21i }{45} = \frac{-3}{5} - \frac{-7}{15}i \)
3. \((-9+8i) \cdot (10-i)= -90+9i +80 i-8i^2 = -90+9i +80 i+8= \color{red}{-90+8}\color{blue}{+9i +80i}=\color{red}{-82}\color{blue}{+89i}\)
4. \((+9i) \cdot (3+6i)= +27 i+54i^2 = \color{red}{-54}\color{blue}{+27i}\)
5. \((4+9i)\cdot (+7i)= +28 i+63i^2 = \color{red}{-63}\color{blue}{+28i}\)
6. \(\frac{-8-i}{7-i}= \frac{-8-i}{7-i} \cdot \frac{7+i}{7+i} = \frac{-56-8i -7 i-i^2 }{(7)^2-(-1i)^2} = \frac{-56-8i -7 i+}{49 + 1} = \frac{-55-15i }{50} = \frac{-11}{10} + \frac{-3}{10}i \)
7. \((+i) \cdot (-6-10i)= -6 i-10i^2 = \color{red}{10}\color{blue}{-6i}\)
8. \((-7i) \cdot (-3-7i)= +21 i+49i^2 = \color{red}{-49}\color{blue}{+21i}\)
9. \((-i) \cdot (6-8i)= -6 i+8i^2 = \color{red}{-8}\color{blue}{-6i}\)
10. \(\frac{-2+9i}{6-3i}= \frac{-2+9i}{6-3i} \cdot \frac{6+3i}{6+3i} = \frac{-12-6i +54 i+27i^2 }{(6)^2-(-3i)^2} = \frac{-12-6i +54 i-27}{36 + 9} = \frac{-39+48i }{45} = \frac{-13}{15} - \frac{-16}{15}i \)
11. \(\frac{-10-8i}{-10-6i}= \frac{-10-8i}{-10-6i} \cdot \frac{-10+6i}{-10+6i} = \frac{100-60i +80 i-48i^2 }{(-10)^2-(-6i)^2} = \frac{100-60i +80 i+48}{100 + 36} = \frac{148+20i }{136} = \frac{37}{34} - \frac{-5}{34}i \)
12. \((-6+7i) \cdot (6+10i)= -36-60i +42 i+70i^2 = -36-60i +42 i-70= \color{red}{-36-70}\color{blue}{-60i +42i}=\color{red}{-106}\color{blue}{-18i}\)