Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \(\frac{-2+2i}{5-i}= \frac{-2+2i}{5-i} \cdot \frac{5+i}{5+i} = \frac{-10-2i +10 i+2i^2 }{(5)^2-(-1i)^2} = \frac{-10-2i +10 i-2}{25 + 1} = \frac{-12+8i }{26} = \frac{-6}{13} - \frac{-4}{13}i \)
2. \((+i) \cdot (-7+2i)= -7 i+2i^2 = \color{red}{-2}\color{blue}{-7i}\)
3. \((-8+8i) \cdot (-10-10i)= 80+80i -80 i-80i^2 = 80+80i -80 i+80= \color{red}{80+80}\color{blue}{+80i -80i}=\color{red}{160}\)
4. \((9+i)\cdot (-6i)= -54 i-6i^2 = \color{red}{6}\color{blue}{-54i}\)
5. \(\frac{-4-9i}{1+6i}= \frac{-4-9i}{1+6i} \cdot \frac{1-6i}{1-6i} = \frac{-4+24i -9 i+54i^2 }{(1)^2-(6i)^2} = \frac{-4+24i -9 i-54}{1 + 36} = \frac{-58+15i }{37} = \frac{-58}{37} - \frac{-15}{37}i \)
6. \((4-5i) \cdot (-7-8i)= -28-32i +35 i+40i^2 = -28-32i +35 i-40= \color{red}{-28-40}\color{blue}{-32i +35i}=\color{red}{-68}\color{blue}{+3i}\)
7. \((-3-10i)\cdot (+3i)= -9 i-30i^2 = \color{red}{30}\color{blue}{-9i}\)
8. \((+6i) \cdot (4+4i)= +24 i+24i^2 = \color{red}{-24}\color{blue}{+24i}\)
9. \((-1-i) \cdot (-8-9i)= 8+9i +8 i+9i^2 = 8+9i +8 i-9= \color{red}{8-9}\color{blue}{+9i +8i}=\color{red}{-1}\color{blue}{+17i}\)
10. \((10-3i) \cdot (-4-9i)= -40-90i +12 i+27i^2 = -40-90i +12 i-27= \color{red}{-40-27}\color{blue}{-90i +12i}=\color{red}{-67}\color{blue}{-78i}\)
11. \((2+9i) \cdot (-7-10i)= -14-20i -63 i-90i^2 = -14-20i -63 i+90= \color{red}{-14+90}\color{blue}{-20i -63i}=\color{red}{76}\color{blue}{-83i}\)
12. \(\frac{6+4i}{-4-5i}= \frac{6+4i}{-4-5i} \cdot \frac{-4+5i}{-4+5i} = \frac{-24+30i -16 i+20i^2 }{(-4)^2-(-5i)^2} = \frac{-24+30i -16 i-20}{16 + 25} = \frac{-44+14i }{41} = \frac{-44}{41} - \frac{-14}{41}i \)