Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \(\frac{6+10i}{-8-10i}= \frac{6+10i}{-8-10i} \cdot \frac{-8+10i}{-8+10i} = \frac{-48+60i -80 i+100i^2 }{(-8)^2-(-10i)^2} = \frac{-48+60i -80 i-100}{64 + 100} = \frac{-148-20i }{164} = \frac{-37}{41} + \frac{-5}{41}i \)
2. \((7+10i)+(5+8i)= 7+10i +5+8i =\color{red}{7+5}\color{blue}{+10i +8i}=\color{red}{12}\color{blue}{+18i}\)
3. \((-9-8i)-(-5+i)= -9-8i +5-i =\color{red}{-9+5}\color{blue}{-8i -i}=\color{red}{-4}\color{blue}{-9i}\)
4. \(\frac{10-6i}{-7+4i}= \frac{10-6i}{-7+4i} \cdot \frac{-7-4i}{-7-4i} = \frac{-70-40i +42 i+24i^2 }{(-7)^2-(4i)^2} = \frac{-70-40i +42 i-24}{49 + 16} = \frac{-94+2i }{65} = \frac{-94}{65} - \frac{-2}{65}i \)
5. \((-8-8i)+(-8-2i)= -8-8i -8-2i =\color{red}{-8-8}\color{blue}{-8i -2i}=\color{red}{-16}\color{blue}{-10i}\)
6. \((-8i) \cdot (-4-5i)= +32 i+40i^2 = \color{red}{-40}\color{blue}{+32i}\)
7. \((-8-7i)+(-5+4i)= -8-7i -5+4i =\color{red}{-8-5}\color{blue}{-7i +4i}=\color{red}{-13}\color{blue}{-3i}\)
8. \(\frac{3-2i}{5+2i}= \frac{3-2i}{5+2i} \cdot \frac{5-2i}{5-2i} = \frac{15-6i -10 i+4i^2 }{(5)^2-(2i)^2} = \frac{15-6i -10 i-4}{25 + 4} = \frac{11-16i }{29} = \frac{11}{29} + \frac{-16}{29}i \)
9. \((4-3i)-(6+3i)= 4-3i -6-3i =\color{red}{4-6}\color{blue}{-3i -3i}=\color{red}{-2}\color{blue}{-6i}\)
10. \((-5+8i) \cdot (-6-7i)= 30+35i -48 i-56i^2 = 30+35i -48 i+56= \color{red}{30+56}\color{blue}{+35i -48i}=\color{red}{86}\color{blue}{-13i}\)
11. \((7-7i)+(-1+10i)= 7-7i -1+10i =\color{red}{7-1}\color{blue}{-7i +10i}=\color{red}{6}\color{blue}{+3i}\)
12. \((-8i) \cdot (2+5i)= -16 i-40i^2 = \color{red}{40}\color{blue}{-16i}\)