Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-6-3i)\cdot (+10i)= -60 i-30i^2 = \color{red}{30}\color{blue}{-60i}\)
2. \(\frac{4-7i}{5-9i}= \frac{4-7i}{5-9i} \cdot \frac{5+9i}{5+9i} = \frac{20+36i -35 i-63i^2 }{(5)^2-(-9i)^2} = \frac{20+36i -35 i+63}{25 + 81} = \frac{83+i }{106} = \frac{83}{106} - \frac{-1}{106}i \)
3. \(\frac{-4-6i}{-7-4i}= \frac{-4-6i}{-7-4i} \cdot \frac{-7+4i}{-7+4i} = \frac{28-16i +42 i-24i^2 }{(-7)^2-(-4i)^2} = \frac{28-16i +42 i+24}{49 + 16} = \frac{52+26i }{65} = \frac{4}{5} - \frac{-2}{5}i \)
4. \((4+3i)\cdot (+9i)= +36 i+27i^2 = \color{red}{-27}\color{blue}{+36i}\)
5. \((-10+8i) \cdot (-6-10i)= 60+100i -48 i-80i^2 = 60+100i -48 i+80= \color{red}{60+80}\color{blue}{+100i -48i}=\color{red}{140}\color{blue}{+52i}\)
6. \((10-8i)\cdot (-2i)= -20 i+16i^2 = \color{red}{-16}\color{blue}{-20i}\)
7. \(\frac{3+4i}{5+6i}= \frac{3+4i}{5+6i} \cdot \frac{5-6i}{5-6i} = \frac{15-18i +20 i-24i^2 }{(5)^2-(6i)^2} = \frac{15-18i +20 i+24}{25 + 36} = \frac{39+2i }{61} = \frac{39}{61} - \frac{-2}{61}i \)
8. \((4+4i)\cdot (-9i)= -36 i-36i^2 = \color{red}{36}\color{blue}{-36i}\)
9. \(\frac{10-9i}{6-8i}= \frac{10-9i}{6-8i} \cdot \frac{6+8i}{6+8i} = \frac{60+80i -54 i-72i^2 }{(6)^2-(-8i)^2} = \frac{60+80i -54 i+72}{36 + 64} = \frac{132+26i }{100} = \frac{33}{25} - \frac{-13}{50}i \)
10. \((7+6i) \cdot (-5-8i)= -35-56i -30 i-48i^2 = -35-56i -30 i+48= \color{red}{-35+48}\color{blue}{-56i -30i}=\color{red}{13}\color{blue}{-86i}\)
11. \(\frac{-8-i}{-3+i}= \frac{-8-i}{-3+i} \cdot \frac{-3-i}{-3-i} = \frac{24+8i +3 i+i^2 }{(-3)^2-(1i)^2} = \frac{24+8i +3 i-}{9 + 1} = \frac{23+11i }{10} = \frac{23}{10} - \frac{-11}{10}i \)
12. \((-9-3i)\cdot (+10i)= -90 i-30i^2 = \color{red}{30}\color{blue}{-90i}\)