Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-8+4i) \cdot (5-5i)= -40+40i +20 i-20i^2 = -40+40i +20 i+20= \color{red}{-40+20}\color{blue}{+40i +20i}=\color{red}{-20}\color{blue}{+60i}\)
2. \((+7i) \cdot (1+4i)= +7 i+28i^2 = \color{red}{-28}\color{blue}{+7i}\)
3. \(\frac{3-2i}{9-2i}= \frac{3-2i}{9-2i} \cdot \frac{9+2i}{9+2i} = \frac{27+6i -18 i-4i^2 }{(9)^2-(-2i)^2} = \frac{27+6i -18 i+4}{81 + 4} = \frac{31-12i }{85} = \frac{31}{85} + \frac{-12}{85}i \)
4. \(\frac{4-2i}{7-6i}= \frac{4-2i}{7-6i} \cdot \frac{7+6i}{7+6i} = \frac{28+24i -14 i-12i^2 }{(7)^2-(-6i)^2} = \frac{28+24i -14 i+12}{49 + 36} = \frac{40+10i }{85} = \frac{8}{17} - \frac{-2}{17}i \)
5. \(\frac{3+i}{8+10i}= \frac{3+i}{8+10i} \cdot \frac{8-10i}{8-10i} = \frac{24-30i +8 i-10i^2 }{(8)^2-(10i)^2} = \frac{24-30i +8 i+10}{64 + 100} = \frac{34-22i }{164} = \frac{17}{82} + \frac{-11}{82}i \)
6. \((10-3i) \cdot (8-i)= 80-10i -24 i+3i^2 = 80-10i -24 i-3= \color{red}{80-3}\color{blue}{-10i -24i}=\color{red}{77}\color{blue}{-34i}\)
7. \(\frac{-9+8i}{-6+9i}= \frac{-9+8i}{-6+9i} \cdot \frac{-6-9i}{-6-9i} = \frac{54+81i -48 i-72i^2 }{(-6)^2-(9i)^2} = \frac{54+81i -48 i+72}{36 + 81} = \frac{126+33i }{117} = \frac{14}{13} - \frac{-11}{39}i \)
8. \((-1+8i) \cdot (-10-9i)= 10+9i -80 i-72i^2 = 10+9i -80 i+72= \color{red}{10+72}\color{blue}{+9i -80i}=\color{red}{82}\color{blue}{-71i}\)
9. \((-2+i) \cdot (7+3i)= -14-6i +7 i+3i^2 = -14-6i +7 i-3= \color{red}{-14-3}\color{blue}{-6i +7i}=\color{red}{-17}\color{blue}{+i}\)
10. \((-2-i) \cdot (-2+2i)= 4-4i +2 i-2i^2 = 4-4i +2 i+2= \color{red}{4+2}\color{blue}{-4i +2i}=\color{red}{6}\color{blue}{-2i}\)
11. \((-6+3i) \cdot (-8-2i)= 48+12i -24 i-6i^2 = 48+12i -24 i+6= \color{red}{48+6}\color{blue}{+12i -24i}=\color{red}{54}\color{blue}{-12i}\)
12. \((-8+2i)\cdot (+3i)= -24 i+6i^2 = \color{red}{-6}\color{blue}{-24i}\)