Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-4+9i)\cdot (+3i)= -12 i+27i^2 = \color{red}{-27}\color{blue}{-12i}\)
2. \((2-3i)\cdot (+4i)= +8 i-12i^2 = \color{red}{12}\color{blue}{+8i}\)
3. \((-10+5i)\cdot (-7i)= +70 i-35i^2 = \color{red}{35}\color{blue}{+70i}\)
4. \((1-5i)-(-8-4i)= 1-5i +8+4i =\color{red}{1+8}\color{blue}{-5i +4i}=\color{red}{9}\color{blue}{-i}\)
5. \((-9-8i) \cdot (-2+8i)= 18-72i +16 i-64i^2 = 18-72i +16 i+64= \color{red}{18+64}\color{blue}{-72i +16i}=\color{red}{82}\color{blue}{-56i}\)
6. \((7-7i)-(-3-7i)= 7-7i +3+7i =\color{red}{7+3}\color{blue}{-7i +7i}=\color{red}{10}\)
7. \(\frac{10-5i}{-4-2i}= \frac{10-5i}{-4-2i} \cdot \frac{-4+2i}{-4+2i} = \frac{-40+20i +20 i-10i^2 }{(-4)^2-(-2i)^2} = \frac{-40+20i +20 i+10}{16 + 4} = \frac{-30+40i }{20} = \frac{-3}{2} - -2i\)
8. \(\frac{-5-4i}{8+10i}= \frac{-5-4i}{8+10i} \cdot \frac{8-10i}{8-10i} = \frac{-40+50i -32 i+40i^2 }{(8)^2-(10i)^2} = \frac{-40+50i -32 i-40}{64 + 100} = \frac{-80+18i }{164} = \frac{-20}{41} - \frac{-9}{82}i \)
9. \(\frac{-3-7i}{-9-4i}= \frac{-3-7i}{-9-4i} \cdot \frac{-9+4i}{-9+4i} = \frac{27-12i +63 i-28i^2 }{(-9)^2-(-4i)^2} = \frac{27-12i +63 i+28}{81 + 16} = \frac{55+51i }{97} = \frac{55}{97} - \frac{-51}{97}i \)
10. \((-8-8i)-(2+8i)= -8-8i -2-8i =\color{red}{-8-2}\color{blue}{-8i -8i}=\color{red}{-10}\color{blue}{-16i}\)
11. \((-2-10i) \cdot (-5+5i)= 10-10i +50 i-50i^2 = 10-10i +50 i+50= \color{red}{10+50}\color{blue}{-10i +50i}=\color{red}{60}\color{blue}{+40i}\)
12. \((+7i) \cdot (-6-i)= -42 i-7i^2 = \color{red}{7}\color{blue}{-42i}\)