Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \(\frac{2-9i}{-6+10i}= \frac{2-9i}{-6+10i} \cdot \frac{-6-10i}{-6-10i} = \frac{-12-20i +54 i+90i^2 }{(-6)^2-(10i)^2} = \frac{-12-20i +54 i-90}{36 + 100} = \frac{-102+34i }{136} = \frac{-3}{4} - \frac{-1}{4}i \)
2. \((8+7i) \cdot (3-9i)= 24-72i +21 i-63i^2 = 24-72i +21 i+63= \color{red}{24+63}\color{blue}{-72i +21i}=\color{red}{87}\color{blue}{-51i}\)
3. \((+i) \cdot (-2+i)= -2 i+i^2 = \color{red}{-1}\color{blue}{-2i}\)
4. \((+9i) \cdot (-4+i)= -36 i+9i^2 = \color{red}{-9}\color{blue}{-36i}\)
5. \((-4-5i)-(-1-3i)= -4-5i +1+3i =\color{red}{-4+1}\color{blue}{-5i +3i}=\color{red}{-3}\color{blue}{-2i}\)
6. \((-9+2i)-(5-5i)= -9+2i -5+5i =\color{red}{-9-5}\color{blue}{+2i +5i}=\color{red}{-14}\color{blue}{+7i}\)
7. \(\frac{-1+8i}{10-10i}= \frac{-1+8i}{10-10i} \cdot \frac{10+10i}{10+10i} = \frac{-10-10i +80 i+80i^2 }{(10)^2-(-10i)^2} = \frac{-10-10i +80 i-80}{100 + 100} = \frac{-90+70i }{200} = \frac{-9}{20} - \frac{-7}{20}i \)
8. \((-2i) \cdot (4-9i)= -8 i+18i^2 = \color{red}{-18}\color{blue}{-8i}\)
9. \((9-6i)+(-3+8i)= 9-6i -3+8i =\color{red}{9-3}\color{blue}{-6i +8i}=\color{red}{6}\color{blue}{+2i}\)
10. \(\frac{-6+i}{-7-i}= \frac{-6+i}{-7-i} \cdot \frac{-7+i}{-7+i} = \frac{42-6i -7 i+i^2 }{(-7)^2-(-1i)^2} = \frac{42-6i -7 i-}{49 + 1} = \frac{41-13i }{50} = \frac{41}{50} + \frac{-13}{50}i \)
11. \(\frac{4+5i}{-2+10i}= \frac{4+5i}{-2+10i} \cdot \frac{-2-10i}{-2-10i} = \frac{-8-40i -10 i-50i^2 }{(-2)^2-(10i)^2} = \frac{-8-40i -10 i+50}{4 + 100} = \frac{42-50i }{104} = \frac{21}{52} + \frac{-25}{52}i \)
12. \((+7i) \cdot (9-4i)= +63 i-28i^2 = \color{red}{28}\color{blue}{+63i}\)