Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-8-5i)+(7+i)= -8-5i +7+i =\color{red}{-8+7}\color{blue}{-5i +i}=\color{red}{-1}\color{blue}{-4i}\)
2. \((-10+6i)\cdot (-6i)= +60 i-36i^2 = \color{red}{36}\color{blue}{+60i}\)
3. \(\frac{-9-6i}{7+8i}= \frac{-9-6i}{7+8i} \cdot \frac{7-8i}{7-8i} = \frac{-63+72i -42 i+48i^2 }{(7)^2-(8i)^2} = \frac{-63+72i -42 i-48}{49 + 64} = \frac{-111+30i }{113} = \frac{-111}{113} - \frac{-30}{113}i \)
4. \(\frac{-4+9i}{2-4i}= \frac{-4+9i}{2-4i} \cdot \frac{2+4i}{2+4i} = \frac{-8-16i +18 i+36i^2 }{(2)^2-(-4i)^2} = \frac{-8-16i +18 i-36}{4 + 16} = \frac{-44+2i }{20} = \frac{-11}{5} - \frac{-1}{10}i \)
5. \((-8+i) \cdot (3+6i)= -24-48i +3 i+6i^2 = -24-48i +3 i-6= \color{red}{-24-6}\color{blue}{-48i +3i}=\color{red}{-30}\color{blue}{-45i}\)
6. \(\frac{9-6i}{2+9i}= \frac{9-6i}{2+9i} \cdot \frac{2-9i}{2-9i} = \frac{18-81i -12 i+54i^2 }{(2)^2-(9i)^2} = \frac{18-81i -12 i-54}{4 + 81} = \frac{-36-93i }{85} = \frac{-36}{85} + \frac{-93}{85}i \)
7. \((3-8i) \cdot (-1+9i)= -3+27i +8 i-72i^2 = -3+27i +8 i+72= \color{red}{-3+72}\color{blue}{+27i +8i}=\color{red}{69}\color{blue}{+35i}\)
8. \((-6+3i) \cdot (-10-10i)= 60+60i -30 i-30i^2 = 60+60i -30 i+30= \color{red}{60+30}\color{blue}{+60i -30i}=\color{red}{90}\color{blue}{+30i}\)
9. \((-9-7i)+(-7+i)= -9-7i -7+i =\color{red}{-9-7}\color{blue}{-7i +i}=\color{red}{-16}\color{blue}{-6i}\)
10. \(\frac{-7-i}{8+6i}= \frac{-7-i}{8+6i} \cdot \frac{8-6i}{8-6i} = \frac{-56+42i -8 i+6i^2 }{(8)^2-(6i)^2} = \frac{-56+42i -8 i-6}{64 + 36} = \frac{-62+34i }{100} = \frac{-31}{50} - \frac{-17}{50}i \)
11. \((-8-9i)-(9+2i)= -8-9i -9-2i =\color{red}{-8-9}\color{blue}{-9i -2i}=\color{red}{-17}\color{blue}{-11i}\)
12. \((-5+9i)+(7-2i)= -5+9i +7-2i =\color{red}{-5+7}\color{blue}{+9i -2i}=\color{red}{2}\color{blue}{+7i}\)