Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-4-5i)+(-1-5i)= -4-5i -1-5i =\color{red}{-4-1}\color{blue}{-5i -5i}=\color{red}{-5}\color{blue}{-10i}\)
2. \((1-2i)+(4-5i)= 1-2i +4-5i =\color{red}{1+4}\color{blue}{-2i -5i}=\color{red}{5}\color{blue}{-7i}\)
3. \((-4-2i) \cdot (2+4i)= -8-16i -4 i-8i^2 = -8-16i -4 i+8= \color{red}{-8+8}\color{blue}{-16i -4i}=\color{blue}{-20i}\)
4. \((-4+8i)-(-4+9i)= -4+8i +4-9i =\color{red}{-4+4}\color{blue}{+8i -9i}=\color{blue}{-i}\)
5. \((-7-5i)-(-5+i)= -7-5i +5-i =\color{red}{-7+5}\color{blue}{-5i -i}=\color{red}{-2}\color{blue}{-6i}\)
6. \((-2-5i)+(-7-7i)= -2-5i -7-7i =\color{red}{-2-7}\color{blue}{-5i -7i}=\color{red}{-9}\color{blue}{-12i}\)
7. \((+10i) \cdot (10-2i)= +100 i-20i^2 = \color{red}{20}\color{blue}{+100i}\)
8. \(\frac{1-4i}{-5+6i}= \frac{1-4i}{-5+6i} \cdot \frac{-5-6i}{-5-6i} = \frac{-5-6i +20 i+24i^2 }{(-5)^2-(6i)^2} = \frac{-5-6i +20 i-24}{25 + 36} = \frac{-29+14i }{61} = \frac{-29}{61} - \frac{-14}{61}i \)
9. \(\frac{-2-6i}{7-3i}= \frac{-2-6i}{7-3i} \cdot \frac{7+3i}{7+3i} = \frac{-14-6i -42 i-18i^2 }{(7)^2-(-3i)^2} = \frac{-14-6i -42 i+18}{49 + 9} = \frac{4-48i }{58} = \frac{2}{29} + \frac{-24}{29}i \)
10. \(\frac{-7-2i}{9+i}= \frac{-7-2i}{9+i} \cdot \frac{9-i}{9-i} = \frac{-63+7i -18 i+2i^2 }{(9)^2-(1i)^2} = \frac{-63+7i -18 i-2}{81 + 1} = \frac{-65-11i }{82} = \frac{-65}{82} + \frac{-11}{82}i \)
11. \(\frac{-3-9i}{-1+7i}= \frac{-3-9i}{-1+7i} \cdot \frac{-1-7i}{-1-7i} = \frac{3+21i +9 i+63i^2 }{(-1)^2-(7i)^2} = \frac{3+21i +9 i-63}{1 + 49} = \frac{-60+30i }{50} = \frac{-6}{5} - \frac{-3}{5}i \)
12. \((9-i)+(-1+3i)= 9-i -1+3i =\color{red}{9-1}\color{blue}{-i +3i}=\color{red}{8}\color{blue}{+2i}\)