Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \(\frac{8+i}{6+2i}= \frac{8+i}{6+2i} \cdot \frac{6-2i}{6-2i} = \frac{48-16i +6 i-2i^2 }{(6)^2-(2i)^2} = \frac{48-16i +6 i+2}{36 + 4} = \frac{50-10i }{40} = \frac{5}{4} + \frac{-1}{4}i \)
2. \((-9-7i) \cdot (8-5i)= -72+45i -56 i+35i^2 = -72+45i -56 i-35= \color{red}{-72-35}\color{blue}{+45i -56i}=\color{red}{-107}\color{blue}{-11i}\)
3. \((-9+9i)+(-10+2i)= -9+9i -10+2i =\color{red}{-9-10}\color{blue}{+9i +2i}=\color{red}{-19}\color{blue}{+11i}\)
4. \((3-8i)-(1-i)= 3-8i -1+i =\color{red}{3-1}\color{blue}{-8i +i}=\color{red}{2}\color{blue}{-7i}\)
5. \((-5-9i)+(2+3i)= -5-9i +2+3i =\color{red}{-5+2}\color{blue}{-9i +3i}=\color{red}{-3}\color{blue}{-6i}\)
6. \(\frac{4+i}{-7-2i}= \frac{4+i}{-7-2i} \cdot \frac{-7+2i}{-7+2i} = \frac{-28+8i -7 i+2i^2 }{(-7)^2-(-2i)^2} = \frac{-28+8i -7 i-2}{49 + 4} = \frac{-30+i }{53} = \frac{-30}{53} - \frac{-1}{53}i \)
7. \((2-10i)+(-9-6i)= 2-10i -9-6i =\color{red}{2-9}\color{blue}{-10i -6i}=\color{red}{-7}\color{blue}{-16i}\)
8. \((5-10i)-(-6+3i)= 5-10i +6-3i =\color{red}{5+6}\color{blue}{-10i -3i}=\color{red}{11}\color{blue}{-13i}\)
9. \((8-3i) \cdot (7-8i)= 56-64i -21 i+24i^2 = 56-64i -21 i-24= \color{red}{56-24}\color{blue}{-64i -21i}=\color{red}{32}\color{blue}{-85i}\)
10. \((+i) \cdot (5-3i)= +5 i-3i^2 = \color{red}{3}\color{blue}{+5i}\)
11. \(\frac{-3+6i}{-10+2i}= \frac{-3+6i}{-10+2i} \cdot \frac{-10-2i}{-10-2i} = \frac{30+6i -60 i-12i^2 }{(-10)^2-(2i)^2} = \frac{30+6i -60 i+12}{100 + 4} = \frac{42-54i }{104} = \frac{21}{52} + \frac{-27}{52}i \)
12. \((-4+4i)\cdot (-7i)= +28 i-28i^2 = \color{red}{28}\color{blue}{+28i}\)