Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-5-7i) \cdot (1+9i)= -5-45i -7 i-63i^2 = -5-45i -7 i+63= \color{red}{-5+63}\color{blue}{-45i -7i}=\color{red}{58}\color{blue}{-52i}\)
2. \((-3+i) \cdot (4-4i)= -12+12i +4 i-4i^2 = -12+12i +4 i+4= \color{red}{-12+4}\color{blue}{+12i +4i}=\color{red}{-8}\color{blue}{+16i}\)
3. \((-3i) \cdot (4+9i)= -12 i-27i^2 = \color{red}{27}\color{blue}{-12i}\)
4. \(\frac{-3+10i}{-3+6i}= \frac{-3+10i}{-3+6i} \cdot \frac{-3-6i}{-3-6i} = \frac{9+18i -30 i-60i^2 }{(-3)^2-(6i)^2} = \frac{9+18i -30 i+60}{9 + 36} = \frac{69-12i }{45} = \frac{23}{15} + \frac{-4}{15}i \)
5. \((-7-7i)\cdot (-4i)= +28 i+28i^2 = \color{red}{-28}\color{blue}{+28i}\)
6. \(\frac{7+3i}{2-6i}= \frac{7+3i}{2-6i} \cdot \frac{2+6i}{2+6i} = \frac{14+42i +6 i+18i^2 }{(2)^2-(-6i)^2} = \frac{14+42i +6 i-18}{4 + 36} = \frac{-4+48i }{40} = \frac{-1}{10} - \frac{-6}{5}i \)
7. \(\frac{-3-i}{6-i}= \frac{-3-i}{6-i} \cdot \frac{6+i}{6+i} = \frac{-18-3i -6 i-i^2 }{(6)^2-(-1i)^2} = \frac{-18-3i -6 i+}{36 + 1} = \frac{-17-9i }{37} = \frac{-17}{37} + \frac{-9}{37}i \)
8. \(\frac{-8-2i}{3-i}= \frac{-8-2i}{3-i} \cdot \frac{3+i}{3+i} = \frac{-24-8i -6 i-2i^2 }{(3)^2-(-1i)^2} = \frac{-24-8i -6 i+2}{9 + 1} = \frac{-22-14i }{10} = \frac{-11}{5} + \frac{-7}{5}i \)
9. \(\frac{-4+2i}{4+10i}= \frac{-4+2i}{4+10i} \cdot \frac{4-10i}{4-10i} = \frac{-16+40i +8 i-20i^2 }{(4)^2-(10i)^2} = \frac{-16+40i +8 i+20}{16 + 100} = \frac{4+48i }{116} = \frac{1}{29} - \frac{-12}{29}i \)
10. \(\frac{10-i}{-3-2i}= \frac{10-i}{-3-2i} \cdot \frac{-3+2i}{-3+2i} = \frac{-30+20i +3 i-2i^2 }{(-3)^2-(-2i)^2} = \frac{-30+20i +3 i+2}{9 + 4} = \frac{-28+23i }{13} = \frac{-28}{13} - \frac{-23}{13}i \)
11. \(\frac{-9+5i}{-7+2i}= \frac{-9+5i}{-7+2i} \cdot \frac{-7-2i}{-7-2i} = \frac{63+18i -35 i-10i^2 }{(-7)^2-(2i)^2} = \frac{63+18i -35 i+10}{49 + 4} = \frac{73-17i }{53} = \frac{73}{53} + \frac{-17}{53}i \)
12. \(\frac{9+8i}{7+i}= \frac{9+8i}{7+i} \cdot \frac{7-i}{7-i} = \frac{63-9i +56 i-8i^2 }{(7)^2-(1i)^2} = \frac{63-9i +56 i+8}{49 + 1} = \frac{71+47i }{50} = \frac{71}{50} - \frac{-47}{50}i \)