Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((4-5i)\cdot (-9i)= -36 i+45i^2 = \color{red}{-45}\color{blue}{-36i}\)
2. \((-9-10i)+(8-4i)= -9-10i +8-4i =\color{red}{-9+8}\color{blue}{-10i -4i}=\color{red}{-1}\color{blue}{-14i}\)
3. \(\frac{-3+7i}{-9+3i}= \frac{-3+7i}{-9+3i} \cdot \frac{-9-3i}{-9-3i} = \frac{27+9i -63 i-21i^2 }{(-9)^2-(3i)^2} = \frac{27+9i -63 i+21}{81 + 9} = \frac{48-54i }{90} = \frac{8}{15} + \frac{-3}{5}i \)
4. \((-1-5i)-(1-5i)= -1-5i -1+5i =\color{red}{-1-1}\color{blue}{-5i +5i}=\color{red}{-2}\)
5. \((-5-3i) \cdot (-5+4i)= 25-20i +15 i-12i^2 = 25-20i +15 i+12= \color{red}{25+12}\color{blue}{-20i +15i}=\color{red}{37}\color{blue}{-5i}\)
6. \((4-i)\cdot (+4i)= +16 i-4i^2 = \color{red}{4}\color{blue}{+16i}\)
7. \(\frac{6-4i}{-3-i}= \frac{6-4i}{-3-i} \cdot \frac{-3+i}{-3+i} = \frac{-18+6i +12 i-4i^2 }{(-3)^2-(-1i)^2} = \frac{-18+6i +12 i+4}{9 + 1} = \frac{-14+18i }{10} = \frac{-7}{5} - \frac{-9}{5}i \)
8. \((-4-i)+(-7-2i)= -4-i -7-2i =\color{red}{-4-7}\color{blue}{-i -2i}=\color{red}{-11}\color{blue}{-3i}\)
9. \((1+2i) \cdot (-9+6i)= -9+6i -18 i+12i^2 = -9+6i -18 i-12= \color{red}{-9-12}\color{blue}{+6i -18i}=\color{red}{-21}\color{blue}{-12i}\)
10. \((-4i) \cdot (6+10i)= -24 i-40i^2 = \color{red}{40}\color{blue}{-24i}\)
11. \((6-2i)\cdot (+9i)= +54 i-18i^2 = \color{red}{18}\color{blue}{+54i}\)
12. \((8-8i) \cdot (-6-3i)= -48-24i +48 i+24i^2 = -48-24i +48 i-24= \color{red}{-48-24}\color{blue}{-24i +48i}=\color{red}{-72}\color{blue}{+24i}\)