Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((+10i) \cdot (-10-7i)= -100 i-70i^2 = \color{red}{70}\color{blue}{-100i}\)
2. \((-6+3i) \cdot (-4-5i)= 24+30i -12 i-15i^2 = 24+30i -12 i+15= \color{red}{24+15}\color{blue}{+30i -12i}=\color{red}{39}\color{blue}{+18i}\)
3. \(\frac{-9-6i}{-6+10i}= \frac{-9-6i}{-6+10i} \cdot \frac{-6-10i}{-6-10i} = \frac{54+90i +36 i+60i^2 }{(-6)^2-(10i)^2} = \frac{54+90i +36 i-60}{36 + 100} = \frac{-6+126i }{136} = \frac{-3}{68} - \frac{-63}{68}i \)
4. \((-5+7i) \cdot (-2-2i)= 10+10i -14 i-14i^2 = 10+10i -14 i+14= \color{red}{10+14}\color{blue}{+10i -14i}=\color{red}{24}\color{blue}{-4i}\)
5. \(\frac{1+7i}{-3-3i}= \frac{1+7i}{-3-3i} \cdot \frac{-3+3i}{-3+3i} = \frac{-3+3i -21 i+21i^2 }{(-3)^2-(-3i)^2} = \frac{-3+3i -21 i-21}{9 + 9} = \frac{-24-18i }{18} = \frac{-4}{3} + 1i\)
6. \((-1+i) \cdot (-2-9i)= 2+9i -2 i-9i^2 = 2+9i -2 i+9= \color{red}{2+9}\color{blue}{+9i -2i}=\color{red}{11}\color{blue}{+7i}\)
7. \(\frac{-9-8i}{5+9i}= \frac{-9-8i}{5+9i} \cdot \frac{5-9i}{5-9i} = \frac{-45+81i -40 i+72i^2 }{(5)^2-(9i)^2} = \frac{-45+81i -40 i-72}{25 + 81} = \frac{-117+41i }{106} = \frac{-117}{106} - \frac{-41}{106}i \)
8. \(\frac{-7+5i}{3+6i}= \frac{-7+5i}{3+6i} \cdot \frac{3-6i}{3-6i} = \frac{-21+42i +15 i-30i^2 }{(3)^2-(6i)^2} = \frac{-21+42i +15 i+30}{9 + 36} = \frac{9+57i }{45} = \frac{1}{5} - \frac{-19}{15}i \)
9. \((-10-i) \cdot (9-2i)= -90+20i -9 i+2i^2 = -90+20i -9 i-2= \color{red}{-90-2}\color{blue}{+20i -9i}=\color{red}{-92}\color{blue}{+11i}\)
10. \((-9i) \cdot (-6-10i)= +54 i+90i^2 = \color{red}{-90}\color{blue}{+54i}\)
11. \((-3-7i)\cdot (+2i)= -6 i-14i^2 = \color{red}{14}\color{blue}{-6i}\)
12. \((-7i) \cdot (-7-3i)= +49 i+21i^2 = \color{red}{-21}\color{blue}{+49i}\)