Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-5i) \cdot (-5-8i)= +25 i+40i^2 = \color{red}{-40}\color{blue}{+25i}\)
2. \((1-10i)\cdot (-9i)= -9 i+90i^2 = \color{red}{-90}\color{blue}{-9i}\)
3. \((2-7i) \cdot (5-8i)= 10-16i -35 i+56i^2 = 10-16i -35 i-56= \color{red}{10-56}\color{blue}{-16i -35i}=\color{red}{-46}\color{blue}{-51i}\)
4. \((-4i) \cdot (2+i)= -8 i-4i^2 = \color{red}{4}\color{blue}{-8i}\)
5. \(\frac{-5-4i}{1-i}= \frac{-5-4i}{1-i} \cdot \frac{1+i}{1+i} = \frac{-5-5i -4 i-4i^2 }{(1)^2-(-1i)^2} = \frac{-5-5i -4 i+4}{1 + 1} = \frac{-1-9i }{2} = \frac{-1}{2} + \frac{-9}{2}i \)
6. \((+5i) \cdot (2+8i)= +10 i+40i^2 = \color{red}{-40}\color{blue}{+10i}\)
7. \(\frac{4+5i}{-7-5i}= \frac{4+5i}{-7-5i} \cdot \frac{-7+5i}{-7+5i} = \frac{-28+20i -35 i+25i^2 }{(-7)^2-(-5i)^2} = \frac{-28+20i -35 i-25}{49 + 25} = \frac{-53-15i }{74} = \frac{-53}{74} + \frac{-15}{74}i \)
8. \((1-10i)\cdot (+5i)= +5 i-50i^2 = \color{red}{50}\color{blue}{+5i}\)
9. \((5-6i) \cdot (-7+7i)= -35+35i +42 i-42i^2 = -35+35i +42 i+42= \color{red}{-35+42}\color{blue}{+35i +42i}=\color{red}{7}\color{blue}{+77i}\)
10. \((-9+9i)\cdot (-6i)= +54 i-54i^2 = \color{red}{54}\color{blue}{+54i}\)
11. \((+10i) \cdot (10+5i)= +100 i+50i^2 = \color{red}{-50}\color{blue}{+100i}\)
12. \(\frac{6-7i}{-2+10i}= \frac{6-7i}{-2+10i} \cdot \frac{-2-10i}{-2-10i} = \frac{-12-60i +14 i+70i^2 }{(-2)^2-(10i)^2} = \frac{-12-60i +14 i-70}{4 + 100} = \frac{-82-46i }{104} = \frac{-41}{52} + \frac{-23}{52}i \)