Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((4-i) \cdot (5-9i)= 20-36i -5 i+9i^2 = 20-36i -5 i-9= \color{red}{20-9}\color{blue}{-36i -5i}=\color{red}{11}\color{blue}{-41i}\)
2. \(\frac{-3-3i}{-4+2i}= \frac{-3-3i}{-4+2i} \cdot \frac{-4-2i}{-4-2i} = \frac{12+6i +12 i+6i^2 }{(-4)^2-(2i)^2} = \frac{12+6i +12 i-6}{16 + 4} = \frac{6+18i }{20} = \frac{3}{10} - \frac{-9}{10}i \)
3. \(\frac{10-10i}{-5+2i}= \frac{10-10i}{-5+2i} \cdot \frac{-5-2i}{-5-2i} = \frac{-50-20i +50 i+20i^2 }{(-5)^2-(2i)^2} = \frac{-50-20i +50 i-20}{25 + 4} = \frac{-70+30i }{29} = \frac{-70}{29} - \frac{-30}{29}i \)
4. \(\frac{-4-4i}{7-7i}= \frac{-4-4i}{7-7i} \cdot \frac{7+7i}{7+7i} = \frac{-28-28i -28 i-28i^2 }{(7)^2-(-7i)^2} = \frac{-28-28i -28 i+28}{49 + 49} = \frac{0-56i }{98} = 0+ \frac{-4}{7}i \)
5. \(\frac{-4-i}{-10-7i}= \frac{-4-i}{-10-7i} \cdot \frac{-10+7i}{-10+7i} = \frac{40-28i +10 i-7i^2 }{(-10)^2-(-7i)^2} = \frac{40-28i +10 i+7}{100 + 49} = \frac{47-18i }{149} = \frac{47}{149} + \frac{-18}{149}i \)
6. \((-9+i)\cdot (-7i)= +63 i-7i^2 = \color{red}{7}\color{blue}{+63i}\)
7. \((-8+4i)\cdot (+10i)= -80 i+40i^2 = \color{red}{-40}\color{blue}{-80i}\)
8. \((7-4i) \cdot (2-9i)= 14-63i -8 i+36i^2 = 14-63i -8 i-36= \color{red}{14-36}\color{blue}{-63i -8i}=\color{red}{-22}\color{blue}{-71i}\)
9. \(\frac{-8-i}{-8+4i}= \frac{-8-i}{-8+4i} \cdot \frac{-8-4i}{-8-4i} = \frac{64+32i +8 i+4i^2 }{(-8)^2-(4i)^2} = \frac{64+32i +8 i-4}{64 + 16} = \frac{60+40i }{80} = \frac{3}{4} - \frac{-1}{2}i \)
10. \((-1+2i) \cdot (4+i)= -4-i +8 i+2i^2 = -4-i +8 i-2= \color{red}{-4-2}\color{blue}{-i +8i}=\color{red}{-6}\color{blue}{+7i}\)
11. \((+10i) \cdot (2-2i)= +20 i-20i^2 = \color{red}{20}\color{blue}{+20i}\)
12. \((6-4i)\cdot (-6i)= -36 i+24i^2 = \color{red}{-24}\color{blue}{-36i}\)