Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((+i) \cdot (-5-4i)= -5 i-4i^2 = \color{red}{4}\color{blue}{-5i}\)
2. \(\frac{-5-10i}{10+5i}= \frac{-5-10i}{10+5i} \cdot \frac{10-5i}{10-5i} = \frac{-50+25i -100 i+50i^2 }{(10)^2-(5i)^2} = \frac{-50+25i -100 i-50}{100 + 25} = \frac{-100-75i }{125} = \frac{-4}{5} + \frac{-3}{5}i \)
3. \((-2i) \cdot (8-i)= -16 i+2i^2 = \color{red}{-2}\color{blue}{-16i}\)
4. \((+i) \cdot (-10-3i)= -10 i-3i^2 = \color{red}{3}\color{blue}{-10i}\)
5. \((-8-9i)\cdot (-5i)= +40 i+45i^2 = \color{red}{-45}\color{blue}{+40i}\)
6. \(\frac{7+10i}{9-7i}= \frac{7+10i}{9-7i} \cdot \frac{9+7i}{9+7i} = \frac{63+49i +90 i+70i^2 }{(9)^2-(-7i)^2} = \frac{63+49i +90 i-70}{81 + 49} = \frac{-7+139i }{130} = \frac{-7}{130} - \frac{-139}{130}i \)
7. \(\frac{-2+2i}{-9-3i}= \frac{-2+2i}{-9-3i} \cdot \frac{-9+3i}{-9+3i} = \frac{18-6i -18 i+6i^2 }{(-9)^2-(-3i)^2} = \frac{18-6i -18 i-6}{81 + 9} = \frac{12-24i }{90} = \frac{2}{15} + \frac{-4}{15}i \)
8. \((4+5i) \cdot (-7+5i)= -28+20i -35 i+25i^2 = -28+20i -35 i-25= \color{red}{-28-25}\color{blue}{+20i -35i}=\color{red}{-53}\color{blue}{-15i}\)
9. \((5+6i) \cdot (-6-i)= -30-5i -36 i-6i^2 = -30-5i -36 i+6= \color{red}{-30+6}\color{blue}{-5i -36i}=\color{red}{-24}\color{blue}{-41i}\)
10. \(\frac{-10-4i}{-7-i}= \frac{-10-4i}{-7-i} \cdot \frac{-7+i}{-7+i} = \frac{70-10i +28 i-4i^2 }{(-7)^2-(-1i)^2} = \frac{70-10i +28 i+4}{49 + 1} = \frac{74+18i }{50} = \frac{37}{25} - \frac{-9}{25}i \)
11. \((-9i) \cdot (-4-4i)= +36 i+36i^2 = \color{red}{-36}\color{blue}{+36i}\)
12. \(\frac{-3-2i}{-1-8i}= \frac{-3-2i}{-1-8i} \cdot \frac{-1+8i}{-1+8i} = \frac{3-24i +2 i-16i^2 }{(-1)^2-(-8i)^2} = \frac{3-24i +2 i+16}{1 + 64} = \frac{19-22i }{65} = \frac{19}{65} + \frac{-22}{65}i \)