Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((10+7i) \cdot (7+i)= 70+10i +49 i+7i^2 = 70+10i +49 i-7= \color{red}{70-7}\color{blue}{+10i +49i}=\color{red}{63}\color{blue}{+59i}\)
2. \((-3+3i)-(1-2i)= -3+3i -1+2i =\color{red}{-3-1}\color{blue}{+3i +2i}=\color{red}{-4}\color{blue}{+5i}\)
3. \((+4i) \cdot (1+3i)= +4 i+12i^2 = \color{red}{-12}\color{blue}{+4i}\)
4. \((+6i) \cdot (-1+7i)= -6 i+42i^2 = \color{red}{-42}\color{blue}{-6i}\)
5. \(\frac{10+9i}{-3+7i}= \frac{10+9i}{-3+7i} \cdot \frac{-3-7i}{-3-7i} = \frac{-30-70i -27 i-63i^2 }{(-3)^2-(7i)^2} = \frac{-30-70i -27 i+63}{9 + 49} = \frac{33-97i }{58} = \frac{33}{58} + \frac{-97}{58}i \)
6. \((-10-4i)\cdot (+7i)= -70 i-28i^2 = \color{red}{28}\color{blue}{-70i}\)
7. \((-4-8i) \cdot (-5-5i)= 20+20i +40 i+40i^2 = 20+20i +40 i-40= \color{red}{20-40}\color{blue}{+20i +40i}=\color{red}{-20}\color{blue}{+60i}\)
8. \((9+4i)+(5+10i)= 9+4i +5+10i =\color{red}{9+5}\color{blue}{+4i +10i}=\color{red}{14}\color{blue}{+14i}\)
9. \((10-6i)+(-5+9i)= 10-6i -5+9i =\color{red}{10-5}\color{blue}{-6i +9i}=\color{red}{5}\color{blue}{+3i}\)
10. \(\frac{2-5i}{-9+2i}= \frac{2-5i}{-9+2i} \cdot \frac{-9-2i}{-9-2i} = \frac{-18-4i +45 i+10i^2 }{(-9)^2-(2i)^2} = \frac{-18-4i +45 i-10}{81 + 4} = \frac{-28+41i }{85} = \frac{-28}{85} - \frac{-41}{85}i \)
11. \(\frac{7-8i}{-8-6i}= \frac{7-8i}{-8-6i} \cdot \frac{-8+6i}{-8+6i} = \frac{-56+42i +64 i-48i^2 }{(-8)^2-(-6i)^2} = \frac{-56+42i +64 i+48}{64 + 36} = \frac{-8+106i }{100} = \frac{-2}{25} - \frac{-53}{50}i \)
12. \(\frac{-2+5i}{3+10i}= \frac{-2+5i}{3+10i} \cdot \frac{3-10i}{3-10i} = \frac{-6+20i +15 i-50i^2 }{(3)^2-(10i)^2} = \frac{-6+20i +15 i+50}{9 + 100} = \frac{44+35i }{109} = \frac{44}{109} - \frac{-35}{109}i \)