Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \(\frac{9+5i}{-8-8i}= \frac{9+5i}{-8-8i} \cdot \frac{-8+8i}{-8+8i} = \frac{-72+72i -40 i+40i^2 }{(-8)^2-(-8i)^2} = \frac{-72+72i -40 i-40}{64 + 64} = \frac{-112+32i }{128} = \frac{-7}{8} - \frac{-1}{4}i \)
2. \(\frac{2-8i}{2-i}= \frac{2-8i}{2-i} \cdot \frac{2+i}{2+i} = \frac{4+2i -16 i-8i^2 }{(2)^2-(-1i)^2} = \frac{4+2i -16 i+8}{4 + 1} = \frac{12-14i }{5} = \frac{12}{5} + \frac{-14}{5}i \)
3. \(\frac{2-2i}{-5-5i}= \frac{2-2i}{-5-5i} \cdot \frac{-5+5i}{-5+5i} = \frac{-10+10i +10 i-10i^2 }{(-5)^2-(-5i)^2} = \frac{-10+10i +10 i+10}{25 + 25} = \frac{0+20i }{50} = 0- \frac{-2}{5}i \)
4. \((3+10i) \cdot (-3-i)= -9-3i -30 i-10i^2 = -9-3i -30 i+10= \color{red}{-9+10}\color{blue}{-3i -30i}=\color{red}{1}\color{blue}{-33i}\)
5. \((6-9i) \cdot (10+2i)= 60+12i -90 i-18i^2 = 60+12i -90 i+18= \color{red}{60+18}\color{blue}{+12i -90i}=\color{red}{78}\color{blue}{-78i}\)
6. \((-1+10i) \cdot (2-i)= -2+i +20 i-10i^2 = -2+i +20 i+10= \color{red}{-2+10}\color{blue}{+i +20i}=\color{red}{8}\color{blue}{+21i}\)
7. \(\frac{2-i}{2-8i}= \frac{2-i}{2-8i} \cdot \frac{2+8i}{2+8i} = \frac{4+16i -2 i-8i^2 }{(2)^2-(-8i)^2} = \frac{4+16i -2 i+8}{4 + 64} = \frac{12+14i }{68} = \frac{3}{17} - \frac{-7}{34}i \)
8. \((-6i) \cdot (6+8i)= -36 i-48i^2 = \color{red}{48}\color{blue}{-36i}\)
9. \((-10i) \cdot (2-8i)= -20 i+80i^2 = \color{red}{-80}\color{blue}{-20i}\)
10. \((+i) \cdot (1-10i)= +1 i-10i^2 = \color{red}{10}\color{blue}{+i}\)
11. \(\frac{-5-3i}{-9-5i}= \frac{-5-3i}{-9-5i} \cdot \frac{-9+5i}{-9+5i} = \frac{45-25i +27 i-15i^2 }{(-9)^2-(-5i)^2} = \frac{45-25i +27 i+15}{81 + 25} = \frac{60+2i }{106} = \frac{30}{53} - \frac{-1}{53}i \)
12. \(\frac{2-5i}{-5-5i}= \frac{2-5i}{-5-5i} \cdot \frac{-5+5i}{-5+5i} = \frac{-10+10i +25 i-25i^2 }{(-5)^2-(-5i)^2} = \frac{-10+10i +25 i+25}{25 + 25} = \frac{15+35i }{50} = \frac{3}{10} - \frac{-7}{10}i \)