Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-1-8i)+(4-7i)= -1-8i +4-7i =\color{red}{-1+4}\color{blue}{-8i -7i}=\color{red}{3}\color{blue}{-15i}\)
2. \(\frac{1+6i}{3-4i}= \frac{1+6i}{3-4i} \cdot \frac{3+4i}{3+4i} = \frac{3+4i +18 i+24i^2 }{(3)^2-(-4i)^2} = \frac{3+4i +18 i-24}{9 + 16} = \frac{-21+22i }{25} = \frac{-21}{25} - \frac{-22}{25}i \)
3. \((-1+4i)+(-2-2i)= -1+4i -2-2i =\color{red}{-1-2}\color{blue}{+4i -2i}=\color{red}{-3}\color{blue}{+2i}\)
4. \((-i) \cdot (-1-2i)= +1 i+2i^2 = \color{red}{-2}\color{blue}{+i}\)
5. \((9+9i)-(10-5i)= 9+9i -10+5i =\color{red}{9-10}\color{blue}{+9i +5i}=\color{red}{-1}\color{blue}{+14i}\)
6. \((-4+3i) \cdot (-5+4i)= 20-16i -15 i+12i^2 = 20-16i -15 i-12= \color{red}{20-12}\color{blue}{-16i -15i}=\color{red}{8}\color{blue}{-31i}\)
7. \((4-8i) \cdot (-5-6i)= -20-24i +40 i+48i^2 = -20-24i +40 i-48= \color{red}{-20-48}\color{blue}{-24i +40i}=\color{red}{-68}\color{blue}{+16i}\)
8. \(\frac{-9+4i}{10-3i}= \frac{-9+4i}{10-3i} \cdot \frac{10+3i}{10+3i} = \frac{-90-27i +40 i+12i^2 }{(10)^2-(-3i)^2} = \frac{-90-27i +40 i-12}{100 + 9} = \frac{-102+13i }{109} = \frac{-102}{109} - \frac{-13}{109}i \)
9. \((-1-7i)+(-5+5i)= -1-7i -5+5i =\color{red}{-1-5}\color{blue}{-7i +5i}=\color{red}{-6}\color{blue}{-2i}\)
10. \((-6-8i) \cdot (10-8i)= -60+48i -80 i+64i^2 = -60+48i -80 i-64= \color{red}{-60-64}\color{blue}{+48i -80i}=\color{red}{-124}\color{blue}{-32i}\)
11. \((-7i) \cdot (6-9i)= -42 i+63i^2 = \color{red}{-63}\color{blue}{-42i}\)
12. \((4+7i)-(-4+8i)= 4+7i +4-8i =\color{red}{4+4}\color{blue}{+7i -8i}=\color{red}{8}\color{blue}{-i}\)