Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-2+5i) \cdot (7-8i)= -14+16i +35 i-40i^2 = -14+16i +35 i+40= \color{red}{-14+40}\color{blue}{+16i +35i}=\color{red}{26}\color{blue}{+51i}\)
2. \((2-2i)-(-8-3i)= 2-2i +8+3i =\color{red}{2+8}\color{blue}{-2i +3i}=\color{red}{10}\color{blue}{+i}\)
3. \(\frac{6-9i}{8-2i}= \frac{6-9i}{8-2i} \cdot \frac{8+2i}{8+2i} = \frac{48+12i -72 i-18i^2 }{(8)^2-(-2i)^2} = \frac{48+12i -72 i+18}{64 + 4} = \frac{66-60i }{68} = \frac{33}{34} + \frac{-15}{17}i \)
4. \((10+2i)+(10-3i)= 10+2i +10-3i =\color{red}{10+10}\color{blue}{+2i -3i}=\color{red}{20}\color{blue}{-i}\)
5. \((-10-3i)+(1+2i)= -10-3i +1+2i =\color{red}{-10+1}\color{blue}{-3i +2i}=\color{red}{-9}\color{blue}{-i}\)
6. \((-1-6i) \cdot (-10-6i)= 10+6i +60 i+36i^2 = 10+6i +60 i-36= \color{red}{10-36}\color{blue}{+6i +60i}=\color{red}{-26}\color{blue}{+66i}\)
7. \((+i) \cdot (3+5i)= +3 i+5i^2 = \color{red}{-5}\color{blue}{+3i}\)
8. \(\frac{-9-7i}{-6-3i}= \frac{-9-7i}{-6-3i} \cdot \frac{-6+3i}{-6+3i} = \frac{54-27i +42 i-21i^2 }{(-6)^2-(-3i)^2} = \frac{54-27i +42 i+21}{36 + 9} = \frac{75+15i }{45} = \frac{5}{3} - \frac{-1}{3}i \)
9. \(\frac{6+i}{1+2i}= \frac{6+i}{1+2i} \cdot \frac{1-2i}{1-2i} = \frac{6-12i +1 i-2i^2 }{(1)^2-(2i)^2} = \frac{6-12i +1 i+2}{1 + 4} = \frac{8-11i }{5} = \frac{8}{5} + \frac{-11}{5}i \)
10. \((-5+3i)+(4+10i)= -5+3i +4+10i =\color{red}{-5+4}\color{blue}{+3i +10i}=\color{red}{-1}\color{blue}{+13i}\)
11. \((-4-i) \cdot (-6-6i)= 24+24i +6 i+6i^2 = 24+24i +6 i-6= \color{red}{24-6}\color{blue}{+24i +6i}=\color{red}{18}\color{blue}{+30i}\)
12. \((1-4i)-(-5+9i)= 1-4i +5-9i =\color{red}{1+5}\color{blue}{-4i -9i}=\color{red}{6}\color{blue}{-13i}\)