Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-6+5i) \cdot (3-9i)= -18+54i +15 i-45i^2 = -18+54i +15 i+45= \color{red}{-18+45}\color{blue}{+54i +15i}=\color{red}{27}\color{blue}{+69i}\)
2. \(\frac{-2-3i}{-2-8i}= \frac{-2-3i}{-2-8i} \cdot \frac{-2+8i}{-2+8i} = \frac{4-16i +6 i-24i^2 }{(-2)^2-(-8i)^2} = \frac{4-16i +6 i+24}{4 + 64} = \frac{28-10i }{68} = \frac{7}{17} + \frac{-5}{34}i \)
3. \((-4i) \cdot (-6+7i)= +24 i-28i^2 = \color{red}{28}\color{blue}{+24i}\)
4. \((-10-9i) \cdot (1-2i)= -10+20i -9 i+18i^2 = -10+20i -9 i-18= \color{red}{-10-18}\color{blue}{+20i -9i}=\color{red}{-28}\color{blue}{+11i}\)
5. \(\frac{7+4i}{1-5i}= \frac{7+4i}{1-5i} \cdot \frac{1+5i}{1+5i} = \frac{7+35i +4 i+20i^2 }{(1)^2-(-5i)^2} = \frac{7+35i +4 i-20}{1 + 25} = \frac{-13+39i }{26} = \frac{-1}{2} - \frac{-3}{2}i \)
6. \((-5i) \cdot (-6+10i)= +30 i-50i^2 = \color{red}{50}\color{blue}{+30i}\)
7. \(\frac{9+8i}{7+10i}= \frac{9+8i}{7+10i} \cdot \frac{7-10i}{7-10i} = \frac{63-90i +56 i-80i^2 }{(7)^2-(10i)^2} = \frac{63-90i +56 i+80}{49 + 100} = \frac{143-34i }{149} = \frac{143}{149} + \frac{-34}{149}i \)
8. \((-9i) \cdot (3+7i)= -27 i-63i^2 = \color{red}{63}\color{blue}{-27i}\)
9. \(\frac{9+10i}{-6-7i}= \frac{9+10i}{-6-7i} \cdot \frac{-6+7i}{-6+7i} = \frac{-54+63i -60 i+70i^2 }{(-6)^2-(-7i)^2} = \frac{-54+63i -60 i-70}{36 + 49} = \frac{-124+3i }{85} = \frac{-124}{85} - \frac{-3}{85}i \)
10. \(\frac{2+4i}{9-7i}= \frac{2+4i}{9-7i} \cdot \frac{9+7i}{9+7i} = \frac{18+14i +36 i+28i^2 }{(9)^2-(-7i)^2} = \frac{18+14i +36 i-28}{81 + 49} = \frac{-10+50i }{130} = \frac{-1}{13} - \frac{-5}{13}i \)
11. \((3-5i) \cdot (-8+2i)= -24+6i +40 i-10i^2 = -24+6i +40 i+10= \color{red}{-24+10}\color{blue}{+6i +40i}=\color{red}{-14}\color{blue}{+46i}\)
12. \((-6+3i)\cdot (-7i)= +42 i-21i^2 = \color{red}{21}\color{blue}{+42i}\)