Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \(\frac{-8-7i}{6+5i}= \frac{-8-7i}{6+5i} \cdot \frac{6-5i}{6-5i} = \frac{-48+40i -42 i+35i^2 }{(6)^2-(5i)^2} = \frac{-48+40i -42 i-35}{36 + 25} = \frac{-83-2i }{61} = \frac{-83}{61} + \frac{-2}{61}i \)
2. \((4-10i)\cdot (+2i)= +8 i-20i^2 = \color{red}{20}\color{blue}{+8i}\)
3. \((-7-4i) \cdot (-3+3i)= 21-21i +12 i-12i^2 = 21-21i +12 i+12= \color{red}{21+12}\color{blue}{-21i +12i}=\color{red}{33}\color{blue}{-9i}\)
4. \(\frac{4-i}{9+6i}= \frac{4-i}{9+6i} \cdot \frac{9-6i}{9-6i} = \frac{36-24i -9 i+6i^2 }{(9)^2-(6i)^2} = \frac{36-24i -9 i-6}{81 + 36} = \frac{30-33i }{117} = \frac{10}{39} + \frac{-11}{39}i \)
5. \((8-10i)\cdot (+9i)= +72 i-90i^2 = \color{red}{90}\color{blue}{+72i}\)
6. \(\frac{8-7i}{9-8i}= \frac{8-7i}{9-8i} \cdot \frac{9+8i}{9+8i} = \frac{72+64i -63 i-56i^2 }{(9)^2-(-8i)^2} = \frac{72+64i -63 i+56}{81 + 64} = \frac{128+i }{145} = \frac{128}{145} - \frac{-1}{145}i \)
7. \((-10-3i)+(2-10i)= -10-3i +2-10i =\color{red}{-10+2}\color{blue}{-3i -10i}=\color{red}{-8}\color{blue}{-13i}\)
8. \((6-6i)+(-5+10i)= 6-6i -5+10i =\color{red}{6-5}\color{blue}{-6i +10i}=\color{red}{1}\color{blue}{+4i}\)
9. \(\frac{4+10i}{-1+5i}= \frac{4+10i}{-1+5i} \cdot \frac{-1-5i}{-1-5i} = \frac{-4-20i -10 i-50i^2 }{(-1)^2-(5i)^2} = \frac{-4-20i -10 i+50}{1 + 25} = \frac{46-30i }{26} = \frac{23}{13} + \frac{-15}{13}i \)
10. \((-4+9i)+(5-6i)= -4+9i +5-6i =\color{red}{-4+5}\color{blue}{+9i -6i}=\color{red}{1}\color{blue}{+3i}\)
11. \((3+3i)+(3+9i)= 3+3i +3+9i =\color{red}{3+3}\color{blue}{+3i +9i}=\color{red}{6}\color{blue}{+12i}\)
12. \((-8+10i)\cdot (-i)= +8 i-10i^2 = \color{red}{10}\color{blue}{+8i}\)