Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-2-9i)-(-7-7i)= -2-9i +7+7i =\color{red}{-2+7}\color{blue}{-9i +7i}=\color{red}{5}\color{blue}{-2i}\)
2. \((10+6i)-(3-5i)= 10+6i -3+5i =\color{red}{10-3}\color{blue}{+6i +5i}=\color{red}{7}\color{blue}{+11i}\)
3. \((-4-i) \cdot (2+i)= -8-4i -2 i-i^2 = -8-4i -2 i+= \color{red}{-8+1}\color{blue}{-4i -2i}=\color{red}{-7}\color{blue}{-6i}\)
4. \((-10-5i)+(5-i)= -10-5i +5-i =\color{red}{-10+5}\color{blue}{-5i -i}=\color{red}{-5}\color{blue}{-6i}\)
5. \(\frac{4-i}{6-3i}= \frac{4-i}{6-3i} \cdot \frac{6+3i}{6+3i} = \frac{24+12i -6 i-3i^2 }{(6)^2-(-3i)^2} = \frac{24+12i -6 i+3}{36 + 9} = \frac{27+6i }{45} = \frac{3}{5} - \frac{-2}{15}i \)
6. \(\frac{9-10i}{3-10i}= \frac{9-10i}{3-10i} \cdot \frac{3+10i}{3+10i} = \frac{27+90i -30 i-100i^2 }{(3)^2-(-10i)^2} = \frac{27+90i -30 i+100}{9 + 100} = \frac{127+60i }{109} = \frac{127}{109} - \frac{-60}{109}i \)
7. \(\frac{-8-i}{-8+3i}= \frac{-8-i}{-8+3i} \cdot \frac{-8-3i}{-8-3i} = \frac{64+24i +8 i+3i^2 }{(-8)^2-(3i)^2} = \frac{64+24i +8 i-3}{64 + 9} = \frac{61+32i }{73} = \frac{61}{73} - \frac{-32}{73}i \)
8. \(\frac{-7+5i}{6-10i}= \frac{-7+5i}{6-10i} \cdot \frac{6+10i}{6+10i} = \frac{-42-70i +30 i+50i^2 }{(6)^2-(-10i)^2} = \frac{-42-70i +30 i-50}{36 + 100} = \frac{-92-40i }{136} = \frac{-23}{34} + \frac{-5}{17}i \)
9. \((-3-3i)+(-10+5i)= -3-3i -10+5i =\color{red}{-3-10}\color{blue}{-3i +5i}=\color{red}{-13}\color{blue}{+2i}\)
10. \((-3+2i)-(-10-3i)= -3+2i +10+3i =\color{red}{-3+10}\color{blue}{+2i +3i}=\color{red}{7}\color{blue}{+5i}\)
11. \((9-5i) \cdot (-8+3i)= -72+27i +40 i-15i^2 = -72+27i +40 i+15= \color{red}{-72+15}\color{blue}{+27i +40i}=\color{red}{-57}\color{blue}{+67i}\)
12. \((-10-6i)\cdot (-7i)= +70 i+42i^2 = \color{red}{-42}\color{blue}{+70i}\)