Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((8-4i)+(-6-7i)= 8-4i -6-7i =\color{red}{8-6}\color{blue}{-4i -7i}=\color{red}{2}\color{blue}{-11i}\)
2. \(\frac{-5-4i}{-3-2i}= \frac{-5-4i}{-3-2i} \cdot \frac{-3+2i}{-3+2i} = \frac{15-10i +12 i-8i^2 }{(-3)^2-(-2i)^2} = \frac{15-10i +12 i+8}{9 + 4} = \frac{23+2i }{13} = \frac{23}{13} - \frac{-2}{13}i \)
3. \((-2+2i)-(-4+7i)= -2+2i +4-7i =\color{red}{-2+4}\color{blue}{+2i -7i}=\color{red}{2}\color{blue}{-5i}\)
4. \(\frac{-2+i}{-8-2i}= \frac{-2+i}{-8-2i} \cdot \frac{-8+2i}{-8+2i} = \frac{16-4i -8 i+2i^2 }{(-8)^2-(-2i)^2} = \frac{16-4i -8 i-2}{64 + 4} = \frac{14-12i }{68} = \frac{7}{34} + \frac{-3}{17}i \)
5. \((-7i) \cdot (-2+3i)= +14 i-21i^2 = \color{red}{21}\color{blue}{+14i}\)
6. \((-6+10i)+(-5-5i)= -6+10i -5-5i =\color{red}{-6-5}\color{blue}{+10i -5i}=\color{red}{-11}\color{blue}{+5i}\)
7. \((4-10i) \cdot (-8+7i)= -32+28i +80 i-70i^2 = -32+28i +80 i+70= \color{red}{-32+70}\color{blue}{+28i +80i}=\color{red}{38}\color{blue}{+108i}\)
8. \(\frac{-4-10i}{-3-5i}= \frac{-4-10i}{-3-5i} \cdot \frac{-3+5i}{-3+5i} = \frac{12-20i +30 i-50i^2 }{(-3)^2-(-5i)^2} = \frac{12-20i +30 i+50}{9 + 25} = \frac{62+10i }{34} = \frac{31}{17} - \frac{-5}{17}i \)
9. \((-5+i)-(10-6i)= -5+i -10+6i =\color{red}{-5-10}\color{blue}{+i +6i}=\color{red}{-15}\color{blue}{+7i}\)
10. \(\frac{-2+9i}{2+9i}= \frac{-2+9i}{2+9i} \cdot \frac{2-9i}{2-9i} = \frac{-4+18i +18 i-81i^2 }{(2)^2-(9i)^2} = \frac{-4+18i +18 i+81}{4 + 81} = \frac{77+36i }{85} = \frac{77}{85} - \frac{-36}{85}i \)
11. \(\frac{-8-9i}{-6+6i}= \frac{-8-9i}{-6+6i} \cdot \frac{-6-6i}{-6-6i} = \frac{48+48i +54 i+54i^2 }{(-6)^2-(6i)^2} = \frac{48+48i +54 i-54}{36 + 36} = \frac{-6+102i }{72} = \frac{-1}{12} - \frac{-17}{12}i \)
12. \((3+8i) \cdot (7+4i)= 21+12i +56 i+32i^2 = 21+12i +56 i-32= \color{red}{21-32}\color{blue}{+12i +56i}=\color{red}{-11}\color{blue}{+68i}\)