Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-5-10i) \cdot (-9+2i)= 45-10i +90 i-20i^2 = 45-10i +90 i+20= \color{red}{45+20}\color{blue}{-10i +90i}=\color{red}{65}\color{blue}{+80i}\)
2. \(\frac{8-2i}{3+6i}= \frac{8-2i}{3+6i} \cdot \frac{3-6i}{3-6i} = \frac{24-48i -6 i+12i^2 }{(3)^2-(6i)^2} = \frac{24-48i -6 i-12}{9 + 36} = \frac{12-54i }{45} = \frac{4}{15} + \frac{-6}{5}i \)
3. \((-1-6i)-(6+2i)= -1-6i -6-2i =\color{red}{-1-6}\color{blue}{-6i -2i}=\color{red}{-7}\color{blue}{-8i}\)
4. \((-2+4i)+(8+8i)= -2+4i +8+8i =\color{red}{-2+8}\color{blue}{+4i +8i}=\color{red}{6}\color{blue}{+12i}\)
5. \(\frac{-8+6i}{5+i}= \frac{-8+6i}{5+i} \cdot \frac{5-i}{5-i} = \frac{-40+8i +30 i-6i^2 }{(5)^2-(1i)^2} = \frac{-40+8i +30 i+6}{25 + 1} = \frac{-34+38i }{26} = \frac{-17}{13} - \frac{-19}{13}i \)
6. \(\frac{4+5i}{-4+4i}= \frac{4+5i}{-4+4i} \cdot \frac{-4-4i}{-4-4i} = \frac{-16-16i -20 i-20i^2 }{(-4)^2-(4i)^2} = \frac{-16-16i -20 i+20}{16 + 16} = \frac{4-36i }{32} = \frac{1}{8} + \frac{-9}{8}i \)
7. \((-9i) \cdot (2+4i)= -18 i-36i^2 = \color{red}{36}\color{blue}{-18i}\)
8. \((3+3i)+(-7-4i)= 3+3i -7-4i =\color{red}{3-7}\color{blue}{+3i -4i}=\color{red}{-4}\color{blue}{-i}\)
9. \(\frac{-8+10i}{-8-5i}= \frac{-8+10i}{-8-5i} \cdot \frac{-8+5i}{-8+5i} = \frac{64-40i -80 i+50i^2 }{(-8)^2-(-5i)^2} = \frac{64-40i -80 i-50}{64 + 25} = \frac{14-120i }{89} = \frac{14}{89} + \frac{-120}{89}i \)
10. \(\frac{-9-8i}{3-6i}= \frac{-9-8i}{3-6i} \cdot \frac{3+6i}{3+6i} = \frac{-27-54i -24 i-48i^2 }{(3)^2-(-6i)^2} = \frac{-27-54i -24 i+48}{9 + 36} = \frac{21-78i }{45} = \frac{7}{15} + \frac{-26}{15}i \)
11. \((8+2i)-(-7+9i)= 8+2i +7-9i =\color{red}{8+7}\color{blue}{+2i -9i}=\color{red}{15}\color{blue}{-7i}\)
12. \((-8i) \cdot (7-i)= -56 i+8i^2 = \color{red}{-8}\color{blue}{-56i}\)