Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-8-i)+(-6+7i)= -8-i -6+7i =\color{red}{-8-6}\color{blue}{-i +7i}=\color{red}{-14}\color{blue}{+6i}\)
2. \((-6i) \cdot (-7+8i)= +42 i-48i^2 = \color{red}{48}\color{blue}{+42i}\)
3. \(\frac{-9-3i}{-2+6i}= \frac{-9-3i}{-2+6i} \cdot \frac{-2-6i}{-2-6i} = \frac{18+54i +6 i+18i^2 }{(-2)^2-(6i)^2} = \frac{18+54i +6 i-18}{4 + 36} = \frac{0+60i }{40} = 0- \frac{-3}{2}i \)
4. \((-5+10i)-(-4+7i)= -5+10i +4-7i =\color{red}{-5+4}\color{blue}{+10i -7i}=\color{red}{-1}\color{blue}{+3i}\)
5. \((-2+9i)+(2-7i)= -2+9i +2-7i =\color{red}{-2+2}\color{blue}{+9i -7i}=\color{blue}{2i}\)
6. \(\frac{5-8i}{-8+10i}= \frac{5-8i}{-8+10i} \cdot \frac{-8-10i}{-8-10i} = \frac{-40-50i +64 i+80i^2 }{(-8)^2-(10i)^2} = \frac{-40-50i +64 i-80}{64 + 100} = \frac{-120+14i }{164} = \frac{-30}{41} - \frac{-7}{82}i \)
7. \((7+6i) \cdot (4-6i)= 28-42i +24 i-36i^2 = 28-42i +24 i+36= \color{red}{28+36}\color{blue}{-42i +24i}=\color{red}{64}\color{blue}{-18i}\)
8. \((-8-2i)-(3-i)= -8-2i -3+i =\color{red}{-8-3}\color{blue}{-2i +i}=\color{red}{-11}\color{blue}{-i}\)
9. \((1-i)-(-6+9i)= 1-i +6-9i =\color{red}{1+6}\color{blue}{-i -9i}=\color{red}{7}\color{blue}{-10i}\)
10. \(\frac{9+8i}{3-4i}= \frac{9+8i}{3-4i} \cdot \frac{3+4i}{3+4i} = \frac{27+36i +24 i+32i^2 }{(3)^2-(-4i)^2} = \frac{27+36i +24 i-32}{9 + 16} = \frac{-5+60i }{25} = \frac{-1}{5} - \frac{-12}{5}i \)
11. \((-5+9i)\cdot (-8i)= +40 i-72i^2 = \color{red}{72}\color{blue}{+40i}\)
12. \((-4+8i)+(4-i)= -4+8i +4-i =\color{red}{-4+4}\color{blue}{+8i -i}=\color{blue}{7i}\)