Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \(\frac{-4+8i}{7-3i}= \frac{-4+8i}{7-3i} \cdot \frac{7+3i}{7+3i} = \frac{-28-12i +56 i+24i^2 }{(7)^2-(-3i)^2} = \frac{-28-12i +56 i-24}{49 + 9} = \frac{-52+44i }{58} = \frac{-26}{29} - \frac{-22}{29}i \)
2. \(\frac{-7-4i}{-5-4i}= \frac{-7-4i}{-5-4i} \cdot \frac{-5+4i}{-5+4i} = \frac{35-28i +20 i-16i^2 }{(-5)^2-(-4i)^2} = \frac{35-28i +20 i+16}{25 + 16} = \frac{51-8i }{41} = \frac{51}{41} + \frac{-8}{41}i \)
3. \((10-2i)\cdot (-4i)= -40 i+8i^2 = \color{red}{-8}\color{blue}{-40i}\)
4. \((4-3i) \cdot (8-3i)= 32-12i -24 i+9i^2 = 32-12i -24 i-9= \color{red}{32-9}\color{blue}{-12i -24i}=\color{red}{23}\color{blue}{-36i}\)
5. \((-1-3i) \cdot (7+8i)= -7-8i -21 i-24i^2 = -7-8i -21 i+24= \color{red}{-7+24}\color{blue}{-8i -21i}=\color{red}{17}\color{blue}{-29i}\)
6. \((5-7i) \cdot (1-9i)= 5-45i -7 i+63i^2 = 5-45i -7 i-63= \color{red}{5-63}\color{blue}{-45i -7i}=\color{red}{-58}\color{blue}{-52i}\)
7. \((8+10i)\cdot (+6i)= +48 i+60i^2 = \color{red}{-60}\color{blue}{+48i}\)
8. \((-7+8i) \cdot (-8-5i)= 56+35i -64 i-40i^2 = 56+35i -64 i+40= \color{red}{56+40}\color{blue}{+35i -64i}=\color{red}{96}\color{blue}{-29i}\)
9. \((4+10i) \cdot (4+i)= 16+4i +40 i+10i^2 = 16+4i +40 i-10= \color{red}{16-10}\color{blue}{+4i +40i}=\color{red}{6}\color{blue}{+44i}\)
10. \(\frac{6+2i}{-3+8i}= \frac{6+2i}{-3+8i} \cdot \frac{-3-8i}{-3-8i} = \frac{-18-48i -6 i-16i^2 }{(-3)^2-(8i)^2} = \frac{-18-48i -6 i+16}{9 + 64} = \frac{-2-54i }{73} = \frac{-2}{73} + \frac{-54}{73}i \)
11. \(\frac{1-3i}{-1+3i}= \frac{1-3i}{-1+3i} \cdot \frac{-1-3i}{-1-3i} = \frac{-1-3i +3 i+9i^2 }{(-1)^2-(3i)^2} = \frac{-1-3i +3 i-9}{1 + 9} = \frac{-10+0i }{10} = -1+ 0i\)
12. \(\frac{-9-2i}{5+7i}= \frac{-9-2i}{5+7i} \cdot \frac{5-7i}{5-7i} = \frac{-45+63i -10 i+14i^2 }{(5)^2-(7i)^2} = \frac{-45+63i -10 i-14}{25 + 49} = \frac{-59+53i }{74} = \frac{-59}{74} - \frac{-53}{74}i \)