Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \(\frac{-1+i}{8-2i}= \frac{-1+i}{8-2i} \cdot \frac{8+2i}{8+2i} = \frac{-8-2i +8 i+2i^2 }{(8)^2-(-2i)^2} = \frac{-8-2i +8 i-2}{64 + 4} = \frac{-10+6i }{68} = \frac{-5}{34} - \frac{-3}{34}i \)
2. \((+2i) \cdot (-1-8i)= -2 i-16i^2 = \color{red}{16}\color{blue}{-2i}\)
3. \(\frac{2+i}{-6+i}= \frac{2+i}{-6+i} \cdot \frac{-6-i}{-6-i} = \frac{-12-2i -6 i-i^2 }{(-6)^2-(1i)^2} = \frac{-12-2i -6 i+}{36 + 1} = \frac{-11-8i }{37} = \frac{-11}{37} + \frac{-8}{37}i \)
4. \((-3-7i) \cdot (6+9i)= -18-27i -42 i-63i^2 = -18-27i -42 i+63= \color{red}{-18+63}\color{blue}{-27i -42i}=\color{red}{45}\color{blue}{-69i}\)
5. \((-2-5i)\cdot (+2i)= -4 i-10i^2 = \color{red}{10}\color{blue}{-4i}\)
6. \((-6i) \cdot (6+2i)= -36 i-12i^2 = \color{red}{12}\color{blue}{-36i}\)
7. \(\frac{8+7i}{4-6i}= \frac{8+7i}{4-6i} \cdot \frac{4+6i}{4+6i} = \frac{32+48i +28 i+42i^2 }{(4)^2-(-6i)^2} = \frac{32+48i +28 i-42}{16 + 36} = \frac{-10+76i }{52} = \frac{-5}{26} - \frac{-19}{13}i \)
8. \((1-10i) \cdot (-1+6i)= -1+6i +10 i-60i^2 = -1+6i +10 i+60= \color{red}{-1+60}\color{blue}{+6i +10i}=\color{red}{59}\color{blue}{+16i}\)
9. \(\frac{5-9i}{2-i}= \frac{5-9i}{2-i} \cdot \frac{2+i}{2+i} = \frac{10+5i -18 i-9i^2 }{(2)^2-(-1i)^2} = \frac{10+5i -18 i+9}{4 + 1} = \frac{19-13i }{5} = \frac{19}{5} + \frac{-13}{5}i \)
10. \((-4+7i)\cdot (-2i)= +8 i-14i^2 = \color{red}{14}\color{blue}{+8i}\)
11. \(\frac{-10+4i}{5+3i}= \frac{-10+4i}{5+3i} \cdot \frac{5-3i}{5-3i} = \frac{-50+30i +20 i-12i^2 }{(5)^2-(3i)^2} = \frac{-50+30i +20 i+12}{25 + 9} = \frac{-38+50i }{34} = \frac{-19}{17} - \frac{-25}{17}i \)
12. \(\frac{9+6i}{8-4i}= \frac{9+6i}{8-4i} \cdot \frac{8+4i}{8+4i} = \frac{72+36i +48 i+24i^2 }{(8)^2-(-4i)^2} = \frac{72+36i +48 i-24}{64 + 16} = \frac{48+84i }{80} = \frac{3}{5} - \frac{-21}{20}i \)