Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((6-i)\cdot (-7i)= -42 i+7i^2 = \color{red}{-7}\color{blue}{-42i}\)
2. \(\frac{-6+8i}{-7+i}= \frac{-6+8i}{-7+i} \cdot \frac{-7-i}{-7-i} = \frac{42+6i -56 i-8i^2 }{(-7)^2-(1i)^2} = \frac{42+6i -56 i+8}{49 + 1} = \frac{50-50i }{50} = 1+ 1i\)
3. \((+4i) \cdot (-1-3i)= -4 i-12i^2 = \color{red}{12}\color{blue}{-4i}\)
4. \((-8-10i)-(4+6i)= -8-10i -4-6i =\color{red}{-8-4}\color{blue}{-10i -6i}=\color{red}{-12}\color{blue}{-16i}\)
5. \((-9-10i)-(-9+6i)= -9-10i +9-6i =\color{red}{-9+9}\color{blue}{-10i -6i}=\color{blue}{-16i}\)
6. \(\frac{-1+6i}{4+10i}= \frac{-1+6i}{4+10i} \cdot \frac{4-10i}{4-10i} = \frac{-4+10i +24 i-60i^2 }{(4)^2-(10i)^2} = \frac{-4+10i +24 i+60}{16 + 100} = \frac{56+34i }{116} = \frac{14}{29} - \frac{-17}{58}i \)
7. \((6-2i)+(-2+4i)= 6-2i -2+4i =\color{red}{6-2}\color{blue}{-2i +4i}=\color{red}{4}\color{blue}{+2i}\)
8. \(\frac{-2+6i}{-9-7i}= \frac{-2+6i}{-9-7i} \cdot \frac{-9+7i}{-9+7i} = \frac{18-14i -54 i+42i^2 }{(-9)^2-(-7i)^2} = \frac{18-14i -54 i-42}{81 + 49} = \frac{-24-68i }{130} = \frac{-12}{65} + \frac{-34}{65}i \)
9. \((-5-9i)-(2+4i)= -5-9i -2-4i =\color{red}{-5-2}\color{blue}{-9i -4i}=\color{red}{-7}\color{blue}{-13i}\)
10. \((-2+9i)+(1-3i)= -2+9i +1-3i =\color{red}{-2+1}\color{blue}{+9i -3i}=\color{red}{-1}\color{blue}{+6i}\)
11. \((6+10i) \cdot (8-8i)= 48-48i +80 i-80i^2 = 48-48i +80 i+80= \color{red}{48+80}\color{blue}{-48i +80i}=\color{red}{128}\color{blue}{+32i}\)
12. \(\frac{9-3i}{1-7i}= \frac{9-3i}{1-7i} \cdot \frac{1+7i}{1+7i} = \frac{9+63i -3 i-21i^2 }{(1)^2-(-7i)^2} = \frac{9+63i -3 i+21}{1 + 49} = \frac{30+60i }{50} = \frac{3}{5} - \frac{-6}{5}i \)