Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-7-8i)-(-2+9i)= -7-8i +2-9i =\color{red}{-7+2}\color{blue}{-8i -9i}=\color{red}{-5}\color{blue}{-17i}\)
2. \((1+8i)\cdot (-i)= -1 i-8i^2 = \color{red}{8}\color{blue}{-i}\)
3. \((-9-10i)+(-5+6i)= -9-10i -5+6i =\color{red}{-9-5}\color{blue}{-10i +6i}=\color{red}{-14}\color{blue}{-4i}\)
4. \(\frac{6+9i}{-8-6i}= \frac{6+9i}{-8-6i} \cdot \frac{-8+6i}{-8+6i} = \frac{-48+36i -72 i+54i^2 }{(-8)^2-(-6i)^2} = \frac{-48+36i -72 i-54}{64 + 36} = \frac{-102-36i }{100} = \frac{-51}{50} + \frac{-9}{25}i \)
5. \((2-9i)-(7-3i)= 2-9i -7+3i =\color{red}{2-7}\color{blue}{-9i +3i}=\color{red}{-5}\color{blue}{-6i}\)
6. \((-5-10i)+(-7+i)= -5-10i -7+i =\color{red}{-5-7}\color{blue}{-10i +i}=\color{red}{-12}\color{blue}{-9i}\)
7. \((-9+i)-(4+6i)= -9+i -4-6i =\color{red}{-9-4}\color{blue}{+i -6i}=\color{red}{-13}\color{blue}{-5i}\)
8. \(\frac{6-2i}{-7-9i}= \frac{6-2i}{-7-9i} \cdot \frac{-7+9i}{-7+9i} = \frac{-42+54i +14 i-18i^2 }{(-7)^2-(-9i)^2} = \frac{-42+54i +14 i+18}{49 + 81} = \frac{-24+68i }{130} = \frac{-12}{65} - \frac{-34}{65}i \)
9. \((-5-8i)-(-3-7i)= -5-8i +3+7i =\color{red}{-5+3}\color{blue}{-8i +7i}=\color{red}{-2}\color{blue}{-i}\)
10. \((6+5i)+(-1-6i)= 6+5i -1-6i =\color{red}{6-1}\color{blue}{+5i -6i}=\color{red}{5}\color{blue}{-i}\)
11. \((-2-8i) \cdot (-5+i)= 10-2i +40 i-8i^2 = 10-2i +40 i+8= \color{red}{10+8}\color{blue}{-2i +40i}=\color{red}{18}\color{blue}{+38i}\)
12. \((6+2i)+(-4+2i)= 6+2i -4+2i =\color{red}{6-4}\color{blue}{+2i +2i}=\color{red}{2}\color{blue}{+4i}\)