Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \(\frac{1+8i}{-9+6i}= \frac{1+8i}{-9+6i} \cdot \frac{-9-6i}{-9-6i} = \frac{-9-6i -72 i-48i^2 }{(-9)^2-(6i)^2} = \frac{-9-6i -72 i+48}{81 + 36} = \frac{39-78i }{117} = \frac{1}{3} + \frac{-2}{3}i \)
2. \(\frac{-5-9i}{-4-6i}= \frac{-5-9i}{-4-6i} \cdot \frac{-4+6i}{-4+6i} = \frac{20-30i +36 i-54i^2 }{(-4)^2-(-6i)^2} = \frac{20-30i +36 i+54}{16 + 36} = \frac{74+6i }{52} = \frac{37}{26} - \frac{-3}{26}i \)
3. \((+6i) \cdot (-7+i)= -42 i+6i^2 = \color{red}{-6}\color{blue}{-42i}\)
4. \(\frac{7+3i}{-6-5i}= \frac{7+3i}{-6-5i} \cdot \frac{-6+5i}{-6+5i} = \frac{-42+35i -18 i+15i^2 }{(-6)^2-(-5i)^2} = \frac{-42+35i -18 i-15}{36 + 25} = \frac{-57+17i }{61} = \frac{-57}{61} - \frac{-17}{61}i \)
5. \(\frac{5-3i}{-10-9i}= \frac{5-3i}{-10-9i} \cdot \frac{-10+9i}{-10+9i} = \frac{-50+45i +30 i-27i^2 }{(-10)^2-(-9i)^2} = \frac{-50+45i +30 i+27}{100 + 81} = \frac{-23+75i }{181} = \frac{-23}{181} - \frac{-75}{181}i \)
6. \((-4-7i) \cdot (-10+7i)= 40-28i +70 i-49i^2 = 40-28i +70 i+49= \color{red}{40+49}\color{blue}{-28i +70i}=\color{red}{89}\color{blue}{+42i}\)
7. \(\frac{6+6i}{2+2i}= \frac{6+6i}{2+2i} \cdot \frac{2-2i}{2-2i} = \frac{12-12i +12 i-12i^2 }{(2)^2-(2i)^2} = \frac{12-12i +12 i+12}{4 + 4} = \frac{24+0i }{8} = 3+ 0i\)
8. \(\frac{-9-9i}{5+3i}= \frac{-9-9i}{5+3i} \cdot \frac{5-3i}{5-3i} = \frac{-45+27i -45 i+27i^2 }{(5)^2-(3i)^2} = \frac{-45+27i -45 i-27}{25 + 9} = \frac{-72-18i }{34} = \frac{-36}{17} + \frac{-9}{17}i \)
9. \((-i) \cdot (-4-7i)= +4 i+7i^2 = \color{red}{-7}\color{blue}{+4i}\)
10. \((-6+8i) \cdot (6-4i)= -36+24i +48 i-32i^2 = -36+24i +48 i+32= \color{red}{-36+32}\color{blue}{+24i +48i}=\color{red}{-4}\color{blue}{+72i}\)
11. \((+2i) \cdot (-3-5i)= -6 i-10i^2 = \color{red}{10}\color{blue}{-6i}\)
12. \((+10i) \cdot (-8+6i)= -80 i+60i^2 = \color{red}{-60}\color{blue}{-80i}\)