Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((10+i)-(-9-4i)= 10+i +9+4i =\color{red}{10+9}\color{blue}{+i +4i}=\color{red}{19}\color{blue}{+5i}\)
2. \((+8i) \cdot (-2+5i)= -16 i+40i^2 = \color{red}{-40}\color{blue}{-16i}\)
3. \(\frac{-2-10i}{10+7i}= \frac{-2-10i}{10+7i} \cdot \frac{10-7i}{10-7i} = \frac{-20+14i -100 i+70i^2 }{(10)^2-(7i)^2} = \frac{-20+14i -100 i-70}{100 + 49} = \frac{-90-86i }{149} = \frac{-90}{149} + \frac{-86}{149}i \)
4. \((-6i) \cdot (5+9i)= -30 i-54i^2 = \color{red}{54}\color{blue}{-30i}\)
5. \((+i) \cdot (-5-7i)= -5 i-7i^2 = \color{red}{7}\color{blue}{-5i}\)
6. \((3+i)\cdot (+8i)= +24 i+8i^2 = \color{red}{-8}\color{blue}{+24i}\)
7. \((-6+10i)+(-6+10i)= -6+10i -6+10i =\color{red}{-6-6}\color{blue}{+10i +10i}=\color{red}{-12}\color{blue}{+20i}\)
8. \((9-7i) \cdot (2+7i)= 18+63i -14 i-49i^2 = 18+63i -14 i+49= \color{red}{18+49}\color{blue}{+63i -14i}=\color{red}{67}\color{blue}{+49i}\)
9. \((-6-10i) \cdot (-6-3i)= 36+18i +60 i+30i^2 = 36+18i +60 i-30= \color{red}{36-30}\color{blue}{+18i +60i}=\color{red}{6}\color{blue}{+78i}\)
10. \((-2+2i) \cdot (2+6i)= -4-12i +4 i+12i^2 = -4-12i +4 i-12= \color{red}{-4-12}\color{blue}{-12i +4i}=\color{red}{-16}\color{blue}{-8i}\)
11. \(\frac{3+8i}{-3+10i}= \frac{3+8i}{-3+10i} \cdot \frac{-3-10i}{-3-10i} = \frac{-9-30i -24 i-80i^2 }{(-3)^2-(10i)^2} = \frac{-9-30i -24 i+80}{9 + 100} = \frac{71-54i }{109} = \frac{71}{109} + \frac{-54}{109}i \)
12. \((-10-9i) \cdot (3+7i)= -30-70i -27 i-63i^2 = -30-70i -27 i+63= \color{red}{-30+63}\color{blue}{-70i -27i}=\color{red}{33}\color{blue}{-97i}\)