Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-8+6i) \cdot (7+6i)= -56-48i +42 i+36i^2 = -56-48i +42 i-36= \color{red}{-56-36}\color{blue}{-48i +42i}=\color{red}{-92}\color{blue}{-6i}\)
2. \((-1-10i) \cdot (-10-10i)= 10+10i +100 i+100i^2 = 10+10i +100 i-100= \color{red}{10-100}\color{blue}{+10i +100i}=\color{red}{-90}\color{blue}{+110i}\)
3. \((-7-10i)\cdot (+3i)= -21 i-30i^2 = \color{red}{30}\color{blue}{-21i}\)
4. \((-5+8i) \cdot (-9+i)= 45-5i -72 i+8i^2 = 45-5i -72 i-8= \color{red}{45-8}\color{blue}{-5i -72i}=\color{red}{37}\color{blue}{-77i}\)
5. \(\frac{-4-8i}{10+6i}= \frac{-4-8i}{10+6i} \cdot \frac{10-6i}{10-6i} = \frac{-40+24i -80 i+48i^2 }{(10)^2-(6i)^2} = \frac{-40+24i -80 i-48}{100 + 36} = \frac{-88-56i }{136} = \frac{-11}{17} + \frac{-7}{17}i \)
6. \((+5i) \cdot (-2-i)= -10 i-5i^2 = \color{red}{5}\color{blue}{-10i}\)
7. \((-6-10i)-(-7+10i)= -6-10i +7-10i =\color{red}{-6+7}\color{blue}{-10i -10i}=\color{red}{1}\color{blue}{-20i}\)
8. \((6+6i) \cdot (-7-8i)= -42-48i -42 i-48i^2 = -42-48i -42 i+48= \color{red}{-42+48}\color{blue}{-48i -42i}=\color{red}{6}\color{blue}{-90i}\)
9. \((2+2i)-(-7-3i)= 2+2i +7+3i =\color{red}{2+7}\color{blue}{+2i +3i}=\color{red}{9}\color{blue}{+5i}\)
10. \(\frac{2+4i}{6+4i}= \frac{2+4i}{6+4i} \cdot \frac{6-4i}{6-4i} = \frac{12-8i +24 i-16i^2 }{(6)^2-(4i)^2} = \frac{12-8i +24 i+16}{36 + 16} = \frac{28+16i }{52} = \frac{7}{13} - \frac{-4}{13}i \)
11. \((-7i) \cdot (-9+4i)= +63 i-28i^2 = \color{red}{28}\color{blue}{+63i}\)
12. \((-2-6i)+(-2-10i)= -2-6i -2-10i =\color{red}{-2-2}\color{blue}{-6i -10i}=\color{red}{-4}\color{blue}{-16i}\)