Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-10-3i)-(2-7i)= -10-3i -2+7i =\color{red}{-10-2}\color{blue}{-3i +7i}=\color{red}{-12}\color{blue}{+4i}\)
2. \((-10+7i)+(-8+3i)= -10+7i -8+3i =\color{red}{-10-8}\color{blue}{+7i +3i}=\color{red}{-18}\color{blue}{+10i}\)
3. \(\frac{-9-9i}{8-6i}= \frac{-9-9i}{8-6i} \cdot \frac{8+6i}{8+6i} = \frac{-72-54i -72 i-54i^2 }{(8)^2-(-6i)^2} = \frac{-72-54i -72 i+54}{64 + 36} = \frac{-18-126i }{100} = \frac{-9}{50} + \frac{-63}{50}i \)
4. \((4+6i)-(1-i)= 4+6i -1+i =\color{red}{4-1}\color{blue}{+6i +i}=\color{red}{3}\color{blue}{+7i}\)
5. \((-1-2i)+(9+4i)= -1-2i +9+4i =\color{red}{-1+9}\color{blue}{-2i +4i}=\color{red}{8}\color{blue}{+2i}\)
6. \(\frac{-6-4i}{-8-7i}= \frac{-6-4i}{-8-7i} \cdot \frac{-8+7i}{-8+7i} = \frac{48-42i +32 i-28i^2 }{(-8)^2-(-7i)^2} = \frac{48-42i +32 i+28}{64 + 49} = \frac{76-10i }{113} = \frac{76}{113} + \frac{-10}{113}i \)
7. \((-10-5i)+(6+2i)= -10-5i +6+2i =\color{red}{-10+6}\color{blue}{-5i +2i}=\color{red}{-4}\color{blue}{-3i}\)
8. \((10+6i)-(5-i)= 10+6i -5+i =\color{red}{10-5}\color{blue}{+6i +i}=\color{red}{5}\color{blue}{+7i}\)
9. \((+i) \cdot (-8-4i)= -8 i-4i^2 = \color{red}{4}\color{blue}{-8i}\)
10. \((6+2i)-(2-i)= 6+2i -2+i =\color{red}{6-2}\color{blue}{+2i +i}=\color{red}{4}\color{blue}{+3i}\)
11. \((-10+i)\cdot (+7i)= -70 i+7i^2 = \color{red}{-7}\color{blue}{-70i}\)
12. \((1+8i)+(7+4i)= 1+8i +7+4i =\color{red}{1+7}\color{blue}{+8i +4i}=\color{red}{8}\color{blue}{+12i}\)