Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \(\frac{-2-6i}{10-4i}= \frac{-2-6i}{10-4i} \cdot \frac{10+4i}{10+4i} = \frac{-20-8i -60 i-24i^2 }{(10)^2-(-4i)^2} = \frac{-20-8i -60 i+24}{100 + 16} = \frac{4-68i }{116} = \frac{1}{29} + \frac{-17}{29}i \)
2. \(\frac{6-7i}{-1+9i}= \frac{6-7i}{-1+9i} \cdot \frac{-1-9i}{-1-9i} = \frac{-6-54i +7 i+63i^2 }{(-1)^2-(9i)^2} = \frac{-6-54i +7 i-63}{1 + 81} = \frac{-69-47i }{82} = \frac{-69}{82} + \frac{-47}{82}i \)
3. \((-10+9i)\cdot (-6i)= +60 i-54i^2 = \color{red}{54}\color{blue}{+60i}\)
4. \((5+5i) \cdot (-4+3i)= -20+15i -20 i+15i^2 = -20+15i -20 i-15= \color{red}{-20-15}\color{blue}{+15i -20i}=\color{red}{-35}\color{blue}{-5i}\)
5. \((5-3i)+(5+4i)= 5-3i +5+4i =\color{red}{5+5}\color{blue}{-3i +4i}=\color{red}{10}\color{blue}{+i}\)
6. \((6+7i) \cdot (1+3i)= 6+18i +7 i+21i^2 = 6+18i +7 i-21= \color{red}{6-21}\color{blue}{+18i +7i}=\color{red}{-15}\color{blue}{+25i}\)
7. \((8+8i)-(-5-4i)= 8+8i +5+4i =\color{red}{8+5}\color{blue}{+8i +4i}=\color{red}{13}\color{blue}{+12i}\)
8. \((-7+5i)+(9-5i)= -7+5i +9-5i =\color{red}{-7+9}\color{blue}{+5i -5i}=\color{red}{2}\)
9. \((7-6i) \cdot (-7+5i)= -49+35i +42 i-30i^2 = -49+35i +42 i+30= \color{red}{-49+30}\color{blue}{+35i +42i}=\color{red}{-19}\color{blue}{+77i}\)
10. \((-7-10i)\cdot (-9i)= +63 i+90i^2 = \color{red}{-90}\color{blue}{+63i}\)
11. \((10-9i) \cdot (-7+3i)= -70+30i +63 i-27i^2 = -70+30i +63 i+27= \color{red}{-70+27}\color{blue}{+30i +63i}=\color{red}{-43}\color{blue}{+93i}\)
12. \((2+6i) \cdot (7-4i)= 14-8i +42 i-24i^2 = 14-8i +42 i+24= \color{red}{14+24}\color{blue}{-8i +42i}=\color{red}{38}\color{blue}{+34i}\)