Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-3-9i)\cdot (+4i)= -12 i-36i^2 = \color{red}{36}\color{blue}{-12i}\)
2. \(\frac{-1+6i}{-1-8i}= \frac{-1+6i}{-1-8i} \cdot \frac{-1+8i}{-1+8i} = \frac{1-8i -6 i+48i^2 }{(-1)^2-(-8i)^2} = \frac{1-8i -6 i-48}{1 + 64} = \frac{-47-14i }{65} = \frac{-47}{65} + \frac{-14}{65}i \)
3. \((-5-4i) \cdot (-10-i)= 50+5i +40 i+4i^2 = 50+5i +40 i-4= \color{red}{50-4}\color{blue}{+5i +40i}=\color{red}{46}\color{blue}{+45i}\)
4. \(\frac{9+2i}{7+4i}= \frac{9+2i}{7+4i} \cdot \frac{7-4i}{7-4i} = \frac{63-36i +14 i-8i^2 }{(7)^2-(4i)^2} = \frac{63-36i +14 i+8}{49 + 16} = \frac{71-22i }{65} = \frac{71}{65} + \frac{-22}{65}i \)
5. \((-5+10i) \cdot (-4+i)= 20-5i -40 i+10i^2 = 20-5i -40 i-10= \color{red}{20-10}\color{blue}{-5i -40i}=\color{red}{10}\color{blue}{-45i}\)
6. \((4+5i) \cdot (-5-6i)= -20-24i -25 i-30i^2 = -20-24i -25 i+30= \color{red}{-20+30}\color{blue}{-24i -25i}=\color{red}{10}\color{blue}{-49i}\)
7. \(\frac{6-5i}{-8-7i}= \frac{6-5i}{-8-7i} \cdot \frac{-8+7i}{-8+7i} = \frac{-48+42i +40 i-35i^2 }{(-8)^2-(-7i)^2} = \frac{-48+42i +40 i+35}{64 + 49} = \frac{-13+82i }{113} = \frac{-13}{113} - \frac{-82}{113}i \)
8. \(\frac{-7+5i}{-2-4i}= \frac{-7+5i}{-2-4i} \cdot \frac{-2+4i}{-2+4i} = \frac{14-28i -10 i+20i^2 }{(-2)^2-(-4i)^2} = \frac{14-28i -10 i-20}{4 + 16} = \frac{-6-38i }{20} = \frac{-3}{10} + \frac{-19}{10}i \)
9. \(\frac{1+3i}{5-9i}= \frac{1+3i}{5-9i} \cdot \frac{5+9i}{5+9i} = \frac{5+9i +15 i+27i^2 }{(5)^2-(-9i)^2} = \frac{5+9i +15 i-27}{25 + 81} = \frac{-22+24i }{106} = \frac{-11}{53} - \frac{-12}{53}i \)
10. \((-4+8i) \cdot (3-6i)= -12+24i +24 i-48i^2 = -12+24i +24 i+48= \color{red}{-12+48}\color{blue}{+24i +24i}=\color{red}{36}\color{blue}{+48i}\)
11. \((-9+7i) \cdot (1-4i)= -9+36i +7 i-28i^2 = -9+36i +7 i+28= \color{red}{-9+28}\color{blue}{+36i +7i}=\color{red}{19}\color{blue}{+43i}\)
12. \((6-5i) \cdot (10-3i)= 60-18i -50 i+15i^2 = 60-18i -50 i-15= \color{red}{60-15}\color{blue}{-18i -50i}=\color{red}{45}\color{blue}{-68i}\)