Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-10+6i) \cdot (8-i)= -80+10i +48 i-6i^2 = -80+10i +48 i+6= \color{red}{-80+6}\color{blue}{+10i +48i}=\color{red}{-74}\color{blue}{+58i}\)
2. \(\frac{-3+8i}{-9-2i}= \frac{-3+8i}{-9-2i} \cdot \frac{-9+2i}{-9+2i} = \frac{27-6i -72 i+16i^2 }{(-9)^2-(-2i)^2} = \frac{27-6i -72 i-16}{81 + 4} = \frac{11-78i }{85} = \frac{11}{85} + \frac{-78}{85}i \)
3. \(\frac{2-4i}{-4+6i}= \frac{2-4i}{-4+6i} \cdot \frac{-4-6i}{-4-6i} = \frac{-8-12i +16 i+24i^2 }{(-4)^2-(6i)^2} = \frac{-8-12i +16 i-24}{16 + 36} = \frac{-32+4i }{52} = \frac{-8}{13} - \frac{-1}{13}i \)
4. \((-4i) \cdot (-6-5i)= +24 i+20i^2 = \color{red}{-20}\color{blue}{+24i}\)
5. \((-2-8i) \cdot (3-7i)= -6+14i -24 i+56i^2 = -6+14i -24 i-56= \color{red}{-6-56}\color{blue}{+14i -24i}=\color{red}{-62}\color{blue}{-10i}\)
6. \(\frac{5+9i}{1+5i}= \frac{5+9i}{1+5i} \cdot \frac{1-5i}{1-5i} = \frac{5-25i +9 i-45i^2 }{(1)^2-(5i)^2} = \frac{5-25i +9 i+45}{1 + 25} = \frac{50-16i }{26} = \frac{25}{13} + \frac{-8}{13}i \)
7. \((-7-8i) \cdot (-1-2i)= 7+14i +8 i+16i^2 = 7+14i +8 i-16= \color{red}{7-16}\color{blue}{+14i +8i}=\color{red}{-9}\color{blue}{+22i}\)
8. \(\frac{-10-8i}{8-9i}= \frac{-10-8i}{8-9i} \cdot \frac{8+9i}{8+9i} = \frac{-80-90i -64 i-72i^2 }{(8)^2-(-9i)^2} = \frac{-80-90i -64 i+72}{64 + 81} = \frac{-8-154i }{145} = \frac{-8}{145} + \frac{-154}{145}i \)
9. \((-2-5i)\cdot (-6i)= +12 i+30i^2 = \color{red}{-30}\color{blue}{+12i}\)
10. \(\frac{-3-10i}{-9+4i}= \frac{-3-10i}{-9+4i} \cdot \frac{-9-4i}{-9-4i} = \frac{27+12i +90 i+40i^2 }{(-9)^2-(4i)^2} = \frac{27+12i +90 i-40}{81 + 16} = \frac{-13+102i }{97} = \frac{-13}{97} - \frac{-102}{97}i \)
11. \((-7+9i) \cdot (-4+9i)= 28-63i -36 i+81i^2 = 28-63i -36 i-81= \color{red}{28-81}\color{blue}{-63i -36i}=\color{red}{-53}\color{blue}{-99i}\)
12. \((3-9i) \cdot (7-6i)= 21-18i -63 i+54i^2 = 21-18i -63 i-54= \color{red}{21-54}\color{blue}{-18i -63i}=\color{red}{-33}\color{blue}{-81i}\)