Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-4-7i)\cdot (-9i)= +36 i+63i^2 = \color{red}{-63}\color{blue}{+36i}\)
2. \(\frac{6-i}{7+2i}= \frac{6-i}{7+2i} \cdot \frac{7-2i}{7-2i} = \frac{42-12i -7 i+2i^2 }{(7)^2-(2i)^2} = \frac{42-12i -7 i-2}{49 + 4} = \frac{40-19i }{53} = \frac{40}{53} + \frac{-19}{53}i \)
3. \((+9i) \cdot (6-2i)= +54 i-18i^2 = \color{red}{18}\color{blue}{+54i}\)
4. \(\frac{4+i}{2+4i}= \frac{4+i}{2+4i} \cdot \frac{2-4i}{2-4i} = \frac{8-16i +2 i-4i^2 }{(2)^2-(4i)^2} = \frac{8-16i +2 i+4}{4 + 16} = \frac{12-14i }{20} = \frac{3}{5} + \frac{-7}{10}i \)
5. \(\frac{-6-2i}{8+7i}= \frac{-6-2i}{8+7i} \cdot \frac{8-7i}{8-7i} = \frac{-48+42i -16 i+14i^2 }{(8)^2-(7i)^2} = \frac{-48+42i -16 i-14}{64 + 49} = \frac{-62+26i }{113} = \frac{-62}{113} - \frac{-26}{113}i \)
6. \((6-8i)-(-8-7i)= 6-8i +8+7i =\color{red}{6+8}\color{blue}{-8i +7i}=\color{red}{14}\color{blue}{-i}\)
7. \((10-10i) \cdot (7-7i)= 70-70i -70 i+70i^2 = 70-70i -70 i-70= \color{red}{70-70}\color{blue}{-70i -70i}=\color{blue}{-140i}\)
8. \((-1+3i)+(3+6i)= -1+3i +3+6i =\color{red}{-1+3}\color{blue}{+3i +6i}=\color{red}{2}\color{blue}{+9i}\)
9. \((-3-2i)-(3+4i)= -3-2i -3-4i =\color{red}{-3-3}\color{blue}{-2i -4i}=\color{red}{-6}\color{blue}{-6i}\)
10. \((-8+6i)+(-2-8i)= -8+6i -2-8i =\color{red}{-8-2}\color{blue}{+6i -8i}=\color{red}{-10}\color{blue}{-2i}\)
11. \((-10+5i)-(-5-i)= -10+5i +5+i =\color{red}{-10+5}\color{blue}{+5i +i}=\color{red}{-5}\color{blue}{+6i}\)
12. \((+3i) \cdot (-5+7i)= -15 i+21i^2 = \color{red}{-21}\color{blue}{-15i}\)