Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((+10i) \cdot (-9-10i)= -90 i-100i^2 = \color{red}{100}\color{blue}{-90i}\)
2. \((-6+6i)\cdot (-5i)= +30 i-30i^2 = \color{red}{30}\color{blue}{+30i}\)
3. \((7-10i)\cdot (-i)= -7 i+10i^2 = \color{red}{-10}\color{blue}{-7i}\)
4. \(\frac{-5+4i}{7+8i}= \frac{-5+4i}{7+8i} \cdot \frac{7-8i}{7-8i} = \frac{-35+40i +28 i-32i^2 }{(7)^2-(8i)^2} = \frac{-35+40i +28 i+32}{49 + 64} = \frac{-3+68i }{113} = \frac{-3}{113} - \frac{-68}{113}i \)
5. \((1+6i) \cdot (7+8i)= 7+8i +42 i+48i^2 = 7+8i +42 i-48= \color{red}{7-48}\color{blue}{+8i +42i}=\color{red}{-41}\color{blue}{+50i}\)
6. \((+9i) \cdot (4+7i)= +36 i+63i^2 = \color{red}{-63}\color{blue}{+36i}\)
7. \(\frac{9-i}{-4+3i}= \frac{9-i}{-4+3i} \cdot \frac{-4-3i}{-4-3i} = \frac{-36-27i +4 i+3i^2 }{(-4)^2-(3i)^2} = \frac{-36-27i +4 i-3}{16 + 9} = \frac{-39-23i }{25} = \frac{-39}{25} + \frac{-23}{25}i \)
8. \((8-5i) \cdot (5+7i)= 40+56i -25 i-35i^2 = 40+56i -25 i+35= \color{red}{40+35}\color{blue}{+56i -25i}=\color{red}{75}\color{blue}{+31i}\)
9. \((5+7i) \cdot (-6-7i)= -30-35i -42 i-49i^2 = -30-35i -42 i+49= \color{red}{-30+49}\color{blue}{-35i -42i}=\color{red}{19}\color{blue}{-77i}\)
10. \((8+2i) \cdot (6+2i)= 48+16i +12 i+4i^2 = 48+16i +12 i-4= \color{red}{48-4}\color{blue}{+16i +12i}=\color{red}{44}\color{blue}{+28i}\)
11. \((-10+5i) \cdot (-2+4i)= 20-40i -10 i+20i^2 = 20-40i -10 i-20= \color{red}{20-20}\color{blue}{-40i -10i}=\color{blue}{-50i}\)
12. \(\frac{9-8i}{10+i}= \frac{9-8i}{10+i} \cdot \frac{10-i}{10-i} = \frac{90-9i -80 i+8i^2 }{(10)^2-(1i)^2} = \frac{90-9i -80 i-8}{100 + 1} = \frac{82-89i }{101} = \frac{82}{101} + \frac{-89}{101}i \)