Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-4+10i) \cdot (-10+6i)= 40-24i -100 i+60i^2 = 40-24i -100 i-60= \color{red}{40-60}\color{blue}{-24i -100i}=\color{red}{-20}\color{blue}{-124i}\)
2. \(\frac{-1-8i}{-9+9i}= \frac{-1-8i}{-9+9i} \cdot \frac{-9-9i}{-9-9i} = \frac{9+9i +72 i+72i^2 }{(-9)^2-(9i)^2} = \frac{9+9i +72 i-72}{81 + 81} = \frac{-63+81i }{162} = \frac{-7}{18} - \frac{-1}{2}i \)
3. \(\frac{-1+5i}{9-7i}= \frac{-1+5i}{9-7i} \cdot \frac{9+7i}{9+7i} = \frac{-9-7i +45 i+35i^2 }{(9)^2-(-7i)^2} = \frac{-9-7i +45 i-35}{81 + 49} = \frac{-44+38i }{130} = \frac{-22}{65} - \frac{-19}{65}i \)
4. \((-4+3i) \cdot (-9+5i)= 36-20i -27 i+15i^2 = 36-20i -27 i-15= \color{red}{36-15}\color{blue}{-20i -27i}=\color{red}{21}\color{blue}{-47i}\)
5. \(\frac{2+10i}{9+7i}= \frac{2+10i}{9+7i} \cdot \frac{9-7i}{9-7i} = \frac{18-14i +90 i-70i^2 }{(9)^2-(7i)^2} = \frac{18-14i +90 i+70}{81 + 49} = \frac{88+76i }{130} = \frac{44}{65} - \frac{-38}{65}i \)
6. \((5-3i) \cdot (-8+2i)= -40+10i +24 i-6i^2 = -40+10i +24 i+6= \color{red}{-40+6}\color{blue}{+10i +24i}=\color{red}{-34}\color{blue}{+34i}\)
7. \((-3i) \cdot (8-7i)= -24 i+21i^2 = \color{red}{-21}\color{blue}{-24i}\)
8. \((10-9i) \cdot (5-i)= 50-10i -45 i+9i^2 = 50-10i -45 i-9= \color{red}{50-9}\color{blue}{-10i -45i}=\color{red}{41}\color{blue}{-55i}\)
9. \(\frac{6-i}{-9-5i}= \frac{6-i}{-9-5i} \cdot \frac{-9+5i}{-9+5i} = \frac{-54+30i +9 i-5i^2 }{(-9)^2-(-5i)^2} = \frac{-54+30i +9 i+5}{81 + 25} = \frac{-49+39i }{106} = \frac{-49}{106} - \frac{-39}{106}i \)
10. \(\frac{2+7i}{-5+7i}= \frac{2+7i}{-5+7i} \cdot \frac{-5-7i}{-5-7i} = \frac{-10-14i -35 i-49i^2 }{(-5)^2-(7i)^2} = \frac{-10-14i -35 i+49}{25 + 49} = \frac{39-49i }{74} = \frac{39}{74} + \frac{-49}{74}i \)
11. \(\frac{3-2i}{-7+i}= \frac{3-2i}{-7+i} \cdot \frac{-7-i}{-7-i} = \frac{-21-3i +14 i+2i^2 }{(-7)^2-(1i)^2} = \frac{-21-3i +14 i-2}{49 + 1} = \frac{-23+11i }{50} = \frac{-23}{50} - \frac{-11}{50}i \)
12. \((8+6i) \cdot (-9-i)= -72-8i -54 i-6i^2 = -72-8i -54 i+6= \color{red}{-72+6}\color{blue}{-8i -54i}=\color{red}{-66}\color{blue}{-62i}\)