Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-5i) \cdot (-5+2i)= +25 i-10i^2 = \color{red}{10}\color{blue}{+25i}\)
2. \((9+2i) \cdot (9-4i)= 81-36i +18 i-8i^2 = 81-36i +18 i+8= \color{red}{81+8}\color{blue}{-36i +18i}=\color{red}{89}\color{blue}{-18i}\)
3. \((3+10i) \cdot (-5+9i)= -15+27i -50 i+90i^2 = -15+27i -50 i-90= \color{red}{-15-90}\color{blue}{+27i -50i}=\color{red}{-105}\color{blue}{-23i}\)
4. \(\frac{-4+3i}{10+8i}= \frac{-4+3i}{10+8i} \cdot \frac{10-8i}{10-8i} = \frac{-40+32i +30 i-24i^2 }{(10)^2-(8i)^2} = \frac{-40+32i +30 i+24}{100 + 64} = \frac{-16+62i }{164} = \frac{-4}{41} - \frac{-31}{82}i \)
5. \((-6+i) \cdot (2-9i)= -12+54i +2 i-9i^2 = -12+54i +2 i+9= \color{red}{-12+9}\color{blue}{+54i +2i}=\color{red}{-3}\color{blue}{+56i}\)
6. \((+3i) \cdot (2-8i)= +6 i-24i^2 = \color{red}{24}\color{blue}{+6i}\)
7. \((10-6i) \cdot (-8-6i)= -80-60i +48 i+36i^2 = -80-60i +48 i-36= \color{red}{-80-36}\color{blue}{-60i +48i}=\color{red}{-116}\color{blue}{-12i}\)
8. \((8-5i) \cdot (-6+i)= -48+8i +30 i-5i^2 = -48+8i +30 i+5= \color{red}{-48+5}\color{blue}{+8i +30i}=\color{red}{-43}\color{blue}{+38i}\)
9. \(\frac{-3-4i}{7+2i}= \frac{-3-4i}{7+2i} \cdot \frac{7-2i}{7-2i} = \frac{-21+6i -28 i+8i^2 }{(7)^2-(2i)^2} = \frac{-21+6i -28 i-8}{49 + 4} = \frac{-29-22i }{53} = \frac{-29}{53} + \frac{-22}{53}i \)
10. \((+7i) \cdot (10-5i)= +70 i-35i^2 = \color{red}{35}\color{blue}{+70i}\)
11. \((-8+i)\cdot (+9i)= -72 i+9i^2 = \color{red}{-9}\color{blue}{-72i}\)
12. \(\frac{-4-8i}{5+3i}= \frac{-4-8i}{5+3i} \cdot \frac{5-3i}{5-3i} = \frac{-20+12i -40 i+24i^2 }{(5)^2-(3i)^2} = \frac{-20+12i -40 i-24}{25 + 9} = \frac{-44-28i }{34} = \frac{-22}{17} + \frac{-14}{17}i \)