Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \(\frac{-8+2i}{-9-4i}= \frac{-8+2i}{-9-4i} \cdot \frac{-9+4i}{-9+4i} = \frac{72-32i -18 i+8i^2 }{(-9)^2-(-4i)^2} = \frac{72-32i -18 i-8}{81 + 16} = \frac{64-50i }{97} = \frac{64}{97} + \frac{-50}{97}i \)
2. \((-4+4i) \cdot (8-8i)= -32+32i +32 i-32i^2 = -32+32i +32 i+32= \color{red}{-32+32}\color{blue}{+32i +32i}=\color{blue}{64i}\)
3. \((9-5i) \cdot (5+9i)= 45+81i -25 i-45i^2 = 45+81i -25 i+45= \color{red}{45+45}\color{blue}{+81i -25i}=\color{red}{90}\color{blue}{+56i}\)
4. \((+10i) \cdot (-4+i)= -40 i+10i^2 = \color{red}{-10}\color{blue}{-40i}\)
5. \(\frac{10+5i}{2+5i}= \frac{10+5i}{2+5i} \cdot \frac{2-5i}{2-5i} = \frac{20-50i +10 i-25i^2 }{(2)^2-(5i)^2} = \frac{20-50i +10 i+25}{4 + 25} = \frac{45-40i }{29} = \frac{45}{29} + \frac{-40}{29}i \)
6. \(\frac{-4-i}{10-9i}= \frac{-4-i}{10-9i} \cdot \frac{10+9i}{10+9i} = \frac{-40-36i -10 i-9i^2 }{(10)^2-(-9i)^2} = \frac{-40-36i -10 i+9}{100 + 81} = \frac{-31-46i }{181} = \frac{-31}{181} + \frac{-46}{181}i \)
7. \(\frac{-4+10i}{10+10i}= \frac{-4+10i}{10+10i} \cdot \frac{10-10i}{10-10i} = \frac{-40+40i +100 i-100i^2 }{(10)^2-(10i)^2} = \frac{-40+40i +100 i+100}{100 + 100} = \frac{60+140i }{200} = \frac{3}{10} - \frac{-7}{10}i \)
8. \((9+8i) \cdot (-10+4i)= -90+36i -80 i+32i^2 = -90+36i -80 i-32= \color{red}{-90-32}\color{blue}{+36i -80i}=\color{red}{-122}\color{blue}{-44i}\)
9. \(\frac{10+5i}{-5-8i}= \frac{10+5i}{-5-8i} \cdot \frac{-5+8i}{-5+8i} = \frac{-50+80i -25 i+40i^2 }{(-5)^2-(-8i)^2} = \frac{-50+80i -25 i-40}{25 + 64} = \frac{-90+55i }{89} = \frac{-90}{89} - \frac{-55}{89}i \)
10. \((+3i) \cdot (-7-4i)= -21 i-12i^2 = \color{red}{12}\color{blue}{-21i}\)
11. \(\frac{-6+3i}{2+9i}= \frac{-6+3i}{2+9i} \cdot \frac{2-9i}{2-9i} = \frac{-12+54i +6 i-27i^2 }{(2)^2-(9i)^2} = \frac{-12+54i +6 i+27}{4 + 81} = \frac{15+60i }{85} = \frac{3}{17} - \frac{-12}{17}i \)
12. \(\frac{2+7i}{-10+2i}= \frac{2+7i}{-10+2i} \cdot \frac{-10-2i}{-10-2i} = \frac{-20-4i -70 i-14i^2 }{(-10)^2-(2i)^2} = \frac{-20-4i -70 i+14}{100 + 4} = \frac{-6-74i }{104} = \frac{-3}{52} + \frac{-37}{52}i \)