Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \(\frac{-3-8i}{-6+10i}= \frac{-3-8i}{-6+10i} \cdot \frac{-6-10i}{-6-10i} = \frac{18+30i +48 i+80i^2 }{(-6)^2-(10i)^2} = \frac{18+30i +48 i-80}{36 + 100} = \frac{-62+78i }{136} = \frac{-31}{68} - \frac{-39}{68}i \)
2. \((-10-4i) \cdot (-6-3i)= 60+30i +24 i+12i^2 = 60+30i +24 i-12= \color{red}{60-12}\color{blue}{+30i +24i}=\color{red}{48}\color{blue}{+54i}\)
3. \((-4+3i)-(-2+8i)= -4+3i +2-8i =\color{red}{-4+2}\color{blue}{+3i -8i}=\color{red}{-2}\color{blue}{-5i}\)
4. \((+5i) \cdot (6-10i)= +30 i-50i^2 = \color{red}{50}\color{blue}{+30i}\)
5. \((-9+4i)-(1-7i)= -9+4i -1+7i =\color{red}{-9-1}\color{blue}{+4i +7i}=\color{red}{-10}\color{blue}{+11i}\)
6. \((8-5i)+(1+4i)= 8-5i +1+4i =\color{red}{8+1}\color{blue}{-5i +4i}=\color{red}{9}\color{blue}{-i}\)
7. \(\frac{2-i}{8-4i}= \frac{2-i}{8-4i} \cdot \frac{8+4i}{8+4i} = \frac{16+8i -8 i-4i^2 }{(8)^2-(-4i)^2} = \frac{16+8i -8 i+4}{64 + 16} = \frac{20+0i }{80} = \frac{1}{4} + 0i\)
8. \((-3-2i)\cdot (-3i)= +9 i+6i^2 = \color{red}{-6}\color{blue}{+9i}\)
9. \((-10+5i)-(-8+9i)= -10+5i +8-9i =\color{red}{-10+8}\color{blue}{+5i -9i}=\color{red}{-2}\color{blue}{-4i}\)
10. \((5+9i)-(-1+7i)= 5+9i +1-7i =\color{red}{5+1}\color{blue}{+9i -7i}=\color{red}{6}\color{blue}{+2i}\)
11. \((-10-6i)\cdot (-8i)= +80 i+48i^2 = \color{red}{-48}\color{blue}{+80i}\)
12. \((3+2i)+(-5+6i)= 3+2i -5+6i =\color{red}{3-5}\color{blue}{+2i +6i}=\color{red}{-2}\color{blue}{+8i}\)