Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \(\frac{8+8i}{-9+4i}= \frac{8+8i}{-9+4i} \cdot \frac{-9-4i}{-9-4i} = \frac{-72-32i -72 i-32i^2 }{(-9)^2-(4i)^2} = \frac{-72-32i -72 i+32}{81 + 16} = \frac{-40-104i }{97} = \frac{-40}{97} + \frac{-104}{97}i \)
2. \((5+4i) \cdot (8+5i)= 40+25i +32 i+20i^2 = 40+25i +32 i-20= \color{red}{40-20}\color{blue}{+25i +32i}=\color{red}{20}\color{blue}{+57i}\)
3. \((4+3i) \cdot (3+8i)= 12+32i +9 i+24i^2 = 12+32i +9 i-24= \color{red}{12-24}\color{blue}{+32i +9i}=\color{red}{-12}\color{blue}{+41i}\)
4. \(\frac{3-10i}{-4-10i}= \frac{3-10i}{-4-10i} \cdot \frac{-4+10i}{-4+10i} = \frac{-12+30i +40 i-100i^2 }{(-4)^2-(-10i)^2} = \frac{-12+30i +40 i+100}{16 + 100} = \frac{88+70i }{116} = \frac{22}{29} - \frac{-35}{58}i \)
5. \((10-7i)\cdot (+4i)= +40 i-28i^2 = \color{red}{28}\color{blue}{+40i}\)
6. \(\frac{-2-4i}{-9+10i}= \frac{-2-4i}{-9+10i} \cdot \frac{-9-10i}{-9-10i} = \frac{18+20i +36 i+40i^2 }{(-9)^2-(10i)^2} = \frac{18+20i +36 i-40}{81 + 100} = \frac{-22+56i }{181} = \frac{-22}{181} - \frac{-56}{181}i \)
7. \((-1+i)\cdot (-5i)= +5 i-5i^2 = \color{red}{5}\color{blue}{+5i}\)
8. \(\frac{5-4i}{-10+3i}= \frac{5-4i}{-10+3i} \cdot \frac{-10-3i}{-10-3i} = \frac{-50-15i +40 i+12i^2 }{(-10)^2-(3i)^2} = \frac{-50-15i +40 i-12}{100 + 9} = \frac{-62+25i }{109} = \frac{-62}{109} - \frac{-25}{109}i \)
9. \((6+4i) \cdot (-10-2i)= -60-12i -40 i-8i^2 = -60-12i -40 i+8= \color{red}{-60+8}\color{blue}{-12i -40i}=\color{red}{-52}\color{blue}{-52i}\)
10. \((8+9i)\cdot (-i)= -8 i-9i^2 = \color{red}{9}\color{blue}{-8i}\)
11. \(\frac{7-6i}{-4-3i}= \frac{7-6i}{-4-3i} \cdot \frac{-4+3i}{-4+3i} = \frac{-28+21i +24 i-18i^2 }{(-4)^2-(-3i)^2} = \frac{-28+21i +24 i+18}{16 + 9} = \frac{-10+45i }{25} = \frac{-2}{5} - \frac{-9}{5}i \)
12. \((-3+10i) \cdot (-1+3i)= 3-9i -10 i+30i^2 = 3-9i -10 i-30= \color{red}{3-30}\color{blue}{-9i -10i}=\color{red}{-27}\color{blue}{-19i}\)