Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \(\frac{-5+9i}{1+8i}= \frac{-5+9i}{1+8i} \cdot \frac{1-8i}{1-8i} = \frac{-5+40i +9 i-72i^2 }{(1)^2-(8i)^2} = \frac{-5+40i +9 i+72}{1 + 64} = \frac{67+49i }{65} = \frac{67}{65} - \frac{-49}{65}i \)
2. \((+10i) \cdot (10-9i)= +100 i-90i^2 = \color{red}{90}\color{blue}{+100i}\)
3. \((+10i) \cdot (2-6i)= +20 i-60i^2 = \color{red}{60}\color{blue}{+20i}\)
4. \((7+6i)+(-5+4i)= 7+6i -5+4i =\color{red}{7-5}\color{blue}{+6i +4i}=\color{red}{2}\color{blue}{+10i}\)
5. \((9+2i)+(-9-10i)= 9+2i -9-10i =\color{red}{9-9}\color{blue}{+2i -10i}=\color{blue}{-8i}\)
6. \((-1+2i) \cdot (-8+2i)= 8-2i -16 i+4i^2 = 8-2i -16 i-4= \color{red}{8-4}\color{blue}{-2i -16i}=\color{red}{4}\color{blue}{-18i}\)
7. \((-5-6i)-(3-7i)= -5-6i -3+7i =\color{red}{-5-3}\color{blue}{-6i +7i}=\color{red}{-8}\color{blue}{+i}\)
8. \((-5i) \cdot (-8-9i)= +40 i+45i^2 = \color{red}{-45}\color{blue}{+40i}\)
9. \(\frac{-1+i}{-10+5i}= \frac{-1+i}{-10+5i} \cdot \frac{-10-5i}{-10-5i} = \frac{10+5i -10 i-5i^2 }{(-10)^2-(5i)^2} = \frac{10+5i -10 i+5}{100 + 25} = \frac{15-5i }{125} = \frac{3}{25} + \frac{-1}{25}i \)
10. \((-6+6i) \cdot (5+i)= -30-6i +30 i+6i^2 = -30-6i +30 i-6= \color{red}{-30-6}\color{blue}{-6i +30i}=\color{red}{-36}\color{blue}{+24i}\)
11. \(\frac{-7-2i}{-10-10i}= \frac{-7-2i}{-10-10i} \cdot \frac{-10+10i}{-10+10i} = \frac{70-70i +20 i-20i^2 }{(-10)^2-(-10i)^2} = \frac{70-70i +20 i+20}{100 + 100} = \frac{90-50i }{200} = \frac{9}{20} + \frac{-1}{4}i \)
12. \((-10-9i) \cdot (-4+7i)= 40-70i +36 i-63i^2 = 40-70i +36 i+63= \color{red}{40+63}\color{blue}{-70i +36i}=\color{red}{103}\color{blue}{-34i}\)