Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \(\frac{9-8i}{8+5i}= \frac{9-8i}{8+5i} \cdot \frac{8-5i}{8-5i} = \frac{72-45i -64 i+40i^2 }{(8)^2-(5i)^2} = \frac{72-45i -64 i-40}{64 + 25} = \frac{32-109i }{89} = \frac{32}{89} + \frac{-109}{89}i \)
2. \((4+8i) \cdot (-4-10i)= -16-40i -32 i-80i^2 = -16-40i -32 i+80= \color{red}{-16+80}\color{blue}{-40i -32i}=\color{red}{64}\color{blue}{-72i}\)
3. \((1-2i)\cdot (-i)= -1 i+2i^2 = \color{red}{-2}\color{blue}{-i}\)
4. \((+5i) \cdot (-8+5i)= -40 i+25i^2 = \color{red}{-25}\color{blue}{-40i}\)
5. \((7-5i)+(-8+5i)= 7-5i -8+5i =\color{red}{7-8}\color{blue}{-5i +5i}=\color{red}{-1}\)
6. \((-8+9i) \cdot (8-i)= -64+8i +72 i-9i^2 = -64+8i +72 i+9= \color{red}{-64+9}\color{blue}{+8i +72i}=\color{red}{-55}\color{blue}{+80i}\)
7. \((9+3i)-(4-6i)= 9+3i -4+6i =\color{red}{9-4}\color{blue}{+3i +6i}=\color{red}{5}\color{blue}{+9i}\)
8. \((-2i) \cdot (-7-4i)= +14 i+8i^2 = \color{red}{-8}\color{blue}{+14i}\)
9. \((-8-i) \cdot (-5-9i)= 40+72i +5 i+9i^2 = 40+72i +5 i-9= \color{red}{40-9}\color{blue}{+72i +5i}=\color{red}{31}\color{blue}{+77i}\)
10. \(\frac{7+3i}{-5+3i}= \frac{7+3i}{-5+3i} \cdot \frac{-5-3i}{-5-3i} = \frac{-35-21i -15 i-9i^2 }{(-5)^2-(3i)^2} = \frac{-35-21i -15 i+9}{25 + 9} = \frac{-26-36i }{34} = \frac{-13}{17} + \frac{-18}{17}i \)
11. \((-6+7i)+(8-7i)= -6+7i +8-7i =\color{red}{-6+8}\color{blue}{+7i -7i}=\color{red}{2}\)
12. \(\frac{-1-2i}{5+5i}= \frac{-1-2i}{5+5i} \cdot \frac{5-5i}{5-5i} = \frac{-5+5i -10 i+10i^2 }{(5)^2-(5i)^2} = \frac{-5+5i -10 i-10}{25 + 25} = \frac{-15-5i }{50} = \frac{-3}{10} + \frac{-1}{10}i \)