Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-1+6i)\cdot (-3i)= +3 i-18i^2 = \color{red}{18}\color{blue}{+3i}\)
2. \(\frac{-2+7i}{9+8i}= \frac{-2+7i}{9+8i} \cdot \frac{9-8i}{9-8i} = \frac{-18+16i +63 i-56i^2 }{(9)^2-(8i)^2} = \frac{-18+16i +63 i+56}{81 + 64} = \frac{38+79i }{145} = \frac{38}{145} - \frac{-79}{145}i \)
3. \((9-3i) \cdot (2-4i)= 18-36i -6 i+12i^2 = 18-36i -6 i-12= \color{red}{18-12}\color{blue}{-36i -6i}=\color{red}{6}\color{blue}{-42i}\)
4. \(\frac{4+8i}{8+6i}= \frac{4+8i}{8+6i} \cdot \frac{8-6i}{8-6i} = \frac{32-24i +64 i-48i^2 }{(8)^2-(6i)^2} = \frac{32-24i +64 i+48}{64 + 36} = \frac{80+40i }{100} = \frac{4}{5} - \frac{-2}{5}i \)
5. \((-7-9i) \cdot (-2+4i)= 14-28i +18 i-36i^2 = 14-28i +18 i+36= \color{red}{14+36}\color{blue}{-28i +18i}=\color{red}{50}\color{blue}{-10i}\)
6. \(\frac{-2+2i}{5+6i}= \frac{-2+2i}{5+6i} \cdot \frac{5-6i}{5-6i} = \frac{-10+12i +10 i-12i^2 }{(5)^2-(6i)^2} = \frac{-10+12i +10 i+12}{25 + 36} = \frac{2+22i }{61} = \frac{2}{61} - \frac{-22}{61}i \)
7. \(\frac{-4-i}{5-7i}= \frac{-4-i}{5-7i} \cdot \frac{5+7i}{5+7i} = \frac{-20-28i -5 i-7i^2 }{(5)^2-(-7i)^2} = \frac{-20-28i -5 i+7}{25 + 49} = \frac{-13-33i }{74} = \frac{-13}{74} + \frac{-33}{74}i \)
8. \((-2-5i) \cdot (1-i)= -2+2i -5 i+5i^2 = -2+2i -5 i-5= \color{red}{-2-5}\color{blue}{+2i -5i}=\color{red}{-7}\color{blue}{-3i}\)
9. \(\frac{7+5i}{-1+9i}= \frac{7+5i}{-1+9i} \cdot \frac{-1-9i}{-1-9i} = \frac{-7-63i -5 i-45i^2 }{(-1)^2-(9i)^2} = \frac{-7-63i -5 i+45}{1 + 81} = \frac{38-68i }{82} = \frac{19}{41} + \frac{-34}{41}i \)
10. \(\frac{-8-4i}{-5+2i}= \frac{-8-4i}{-5+2i} \cdot \frac{-5-2i}{-5-2i} = \frac{40+16i +20 i+8i^2 }{(-5)^2-(2i)^2} = \frac{40+16i +20 i-8}{25 + 4} = \frac{32+36i }{29} = \frac{32}{29} - \frac{-36}{29}i \)
11. \((8-10i)\cdot (-i)= -8 i+10i^2 = \color{red}{-10}\color{blue}{-8i}\)
12. \(\frac{-3-8i}{7+6i}= \frac{-3-8i}{7+6i} \cdot \frac{7-6i}{7-6i} = \frac{-21+18i -56 i+48i^2 }{(7)^2-(6i)^2} = \frac{-21+18i -56 i-48}{49 + 36} = \frac{-69-38i }{85} = \frac{-69}{85} + \frac{-38}{85}i \)