Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \(\frac{-9-10i}{5-5i}= \frac{-9-10i}{5-5i} \cdot \frac{5+5i}{5+5i} = \frac{-45-45i -50 i-50i^2 }{(5)^2-(-5i)^2} = \frac{-45-45i -50 i+50}{25 + 25} = \frac{5-95i }{50} = \frac{1}{10} + \frac{-19}{10}i \)
2. \((-6-4i) \cdot (3+5i)= -18-30i -12 i-20i^2 = -18-30i -12 i+20= \color{red}{-18+20}\color{blue}{-30i -12i}=\color{red}{2}\color{blue}{-42i}\)
3. \((1-9i)\cdot (+9i)= +9 i-81i^2 = \color{red}{81}\color{blue}{+9i}\)
4. \(\frac{-9+7i}{2-2i}= \frac{-9+7i}{2-2i} \cdot \frac{2+2i}{2+2i} = \frac{-18-18i +14 i+14i^2 }{(2)^2-(-2i)^2} = \frac{-18-18i +14 i-14}{4 + 4} = \frac{-32-4i }{8} = -4+ \frac{-1}{2}i \)
5. \((7+6i)-(3-5i)= 7+6i -3+5i =\color{red}{7-3}\color{blue}{+6i +5i}=\color{red}{4}\color{blue}{+11i}\)
6. \(\frac{-3+10i}{-2+6i}= \frac{-3+10i}{-2+6i} \cdot \frac{-2-6i}{-2-6i} = \frac{6+18i -20 i-60i^2 }{(-2)^2-(6i)^2} = \frac{6+18i -20 i+60}{4 + 36} = \frac{66-2i }{40} = \frac{33}{20} + \frac{-1}{20}i \)
7. \((10+6i)-(-7-3i)= 10+6i +7+3i =\color{red}{10+7}\color{blue}{+6i +3i}=\color{red}{17}\color{blue}{+9i}\)
8. \((-1-7i)\cdot (+2i)= -2 i-14i^2 = \color{red}{14}\color{blue}{-2i}\)
9. \((7+6i)+(4-5i)= 7+6i +4-5i =\color{red}{7+4}\color{blue}{+6i -5i}=\color{red}{11}\color{blue}{+i}\)
10. \((-2+9i)-(-3+3i)= -2+9i +3-3i =\color{red}{-2+3}\color{blue}{+9i -3i}=\color{red}{1}\color{blue}{+6i}\)
11. \((-10+10i)-(-1-5i)= -10+10i +1+5i =\color{red}{-10+1}\color{blue}{+10i +5i}=\color{red}{-9}\color{blue}{+15i}\)
12. \((10+7i)+(5+9i)= 10+7i +5+9i =\color{red}{10+5}\color{blue}{+7i +9i}=\color{red}{15}\color{blue}{+16i}\)