Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((7-3i)+(-5+3i)= 7-3i -5+3i =\color{red}{7-5}\color{blue}{-3i +3i}=\color{red}{2}\)
2. \((7-6i) \cdot (-9+5i)= -63+35i +54 i-30i^2 = -63+35i +54 i+30= \color{red}{-63+30}\color{blue}{+35i +54i}=\color{red}{-33}\color{blue}{+89i}\)
3. \((-8-10i)-(5-6i)= -8-10i -5+6i =\color{red}{-8-5}\color{blue}{-10i +6i}=\color{red}{-13}\color{blue}{-4i}\)
4. \((2-8i) \cdot (8+9i)= 16+18i -64 i-72i^2 = 16+18i -64 i+72= \color{red}{16+72}\color{blue}{+18i -64i}=\color{red}{88}\color{blue}{-46i}\)
5. \((-2-2i)-(4+7i)= -2-2i -4-7i =\color{red}{-2-4}\color{blue}{-2i -7i}=\color{red}{-6}\color{blue}{-9i}\)
6. \((-7+i)+(-7-3i)= -7+i -7-3i =\color{red}{-7-7}\color{blue}{+i -3i}=\color{red}{-14}\color{blue}{-2i}\)
7. \(\frac{-7-8i}{-5-6i}= \frac{-7-8i}{-5-6i} \cdot \frac{-5+6i}{-5+6i} = \frac{35-42i +40 i-48i^2 }{(-5)^2-(-6i)^2} = \frac{35-42i +40 i+48}{25 + 36} = \frac{83-2i }{61} = \frac{83}{61} + \frac{-2}{61}i \)
8. \(\frac{-1-3i}{4-8i}= \frac{-1-3i}{4-8i} \cdot \frac{4+8i}{4+8i} = \frac{-4-8i -12 i-24i^2 }{(4)^2-(-8i)^2} = \frac{-4-8i -12 i+24}{16 + 64} = \frac{20-20i }{80} = \frac{1}{4} + \frac{-1}{4}i \)
9. \((-10i) \cdot (1-5i)= -10 i+50i^2 = \color{red}{-50}\color{blue}{-10i}\)
10. \(\frac{3+3i}{7-7i}= \frac{3+3i}{7-7i} \cdot \frac{7+7i}{7+7i} = \frac{21+21i +21 i+21i^2 }{(7)^2-(-7i)^2} = \frac{21+21i +21 i-21}{49 + 49} = \frac{0+42i }{98} = 0- \frac{-3}{7}i \)
11. \((-8+10i) \cdot (-9+3i)= 72-24i -90 i+30i^2 = 72-24i -90 i-30= \color{red}{72-30}\color{blue}{-24i -90i}=\color{red}{42}\color{blue}{-114i}\)
12. \(\frac{-1-9i}{-1-7i}= \frac{-1-9i}{-1-7i} \cdot \frac{-1+7i}{-1+7i} = \frac{1-7i +9 i-63i^2 }{(-1)^2-(-7i)^2} = \frac{1-7i +9 i+63}{1 + 49} = \frac{64+2i }{50} = \frac{32}{25} - \frac{-1}{25}i \)