Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-6+i)\cdot (-i)= +6 i-i^2 = \color{red}{1}\color{blue}{+6i}\)
2. \(\frac{10+7i}{-5-9i}= \frac{10+7i}{-5-9i} \cdot \frac{-5+9i}{-5+9i} = \frac{-50+90i -35 i+63i^2 }{(-5)^2-(-9i)^2} = \frac{-50+90i -35 i-63}{25 + 81} = \frac{-113+55i }{106} = \frac{-113}{106} - \frac{-55}{106}i \)
3. \((-2+6i)\cdot (+4i)= -8 i+24i^2 = \color{red}{-24}\color{blue}{-8i}\)
4. \((1+2i) \cdot (-1-6i)= -1-6i -2 i-12i^2 = -1-6i -2 i+12= \color{red}{-1+12}\color{blue}{-6i -2i}=\color{red}{11}\color{blue}{-8i}\)
5. \(\frac{1+7i}{-6-10i}= \frac{1+7i}{-6-10i} \cdot \frac{-6+10i}{-6+10i} = \frac{-6+10i -42 i+70i^2 }{(-6)^2-(-10i)^2} = \frac{-6+10i -42 i-70}{36 + 100} = \frac{-76-32i }{136} = \frac{-19}{34} + \frac{-4}{17}i \)
6. \(\frac{-6+5i}{5+10i}= \frac{-6+5i}{5+10i} \cdot \frac{5-10i}{5-10i} = \frac{-30+60i +25 i-50i^2 }{(5)^2-(10i)^2} = \frac{-30+60i +25 i+50}{25 + 100} = \frac{20+85i }{125} = \frac{4}{25} - \frac{-17}{25}i \)
7. \(\frac{-8-i}{2+8i}= \frac{-8-i}{2+8i} \cdot \frac{2-8i}{2-8i} = \frac{-16+64i -2 i+8i^2 }{(2)^2-(8i)^2} = \frac{-16+64i -2 i-8}{4 + 64} = \frac{-24+62i }{68} = \frac{-6}{17} - \frac{-31}{34}i \)
8. \(\frac{5-3i}{8-7i}= \frac{5-3i}{8-7i} \cdot \frac{8+7i}{8+7i} = \frac{40+35i -24 i-21i^2 }{(8)^2-(-7i)^2} = \frac{40+35i -24 i+21}{64 + 49} = \frac{61+11i }{113} = \frac{61}{113} - \frac{-11}{113}i \)
9. \((-6i) \cdot (4+10i)= -24 i-60i^2 = \color{red}{60}\color{blue}{-24i}\)
10. \(\frac{-4-10i}{-2-5i}= \frac{-4-10i}{-2-5i} \cdot \frac{-2+5i}{-2+5i} = \frac{8-20i +20 i-50i^2 }{(-2)^2-(-5i)^2} = \frac{8-20i +20 i+50}{4 + 25} = \frac{58+0i }{29} = 2+ 0i\)
11. \((+4i) \cdot (-6+7i)= -24 i+28i^2 = \color{red}{-28}\color{blue}{-24i}\)
12. \((+9i) \cdot (9-8i)= +81 i-72i^2 = \color{red}{72}\color{blue}{+81i}\)