Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((3-4i)-(2-3i)= 3-4i -2+3i =\color{red}{3-2}\color{blue}{-4i +3i}=\color{red}{1}\color{blue}{-i}\)
2. \((4+9i) \cdot (-6+3i)= -24+12i -54 i+27i^2 = -24+12i -54 i-27= \color{red}{-24-27}\color{blue}{+12i -54i}=\color{red}{-51}\color{blue}{-42i}\)
3. \(\frac{6+6i}{1+3i}= \frac{6+6i}{1+3i} \cdot \frac{1-3i}{1-3i} = \frac{6-18i +6 i-18i^2 }{(1)^2-(3i)^2} = \frac{6-18i +6 i+18}{1 + 9} = \frac{24-12i }{10} = \frac{12}{5} + \frac{-6}{5}i \)
4. \(\frac{8-6i}{-2-3i}= \frac{8-6i}{-2-3i} \cdot \frac{-2+3i}{-2+3i} = \frac{-16+24i +12 i-18i^2 }{(-2)^2-(-3i)^2} = \frac{-16+24i +12 i+18}{4 + 9} = \frac{2+36i }{13} = \frac{2}{13} - \frac{-36}{13}i \)
5. \(\frac{-7-3i}{5-9i}= \frac{-7-3i}{5-9i} \cdot \frac{5+9i}{5+9i} = \frac{-35-63i -15 i-27i^2 }{(5)^2-(-9i)^2} = \frac{-35-63i -15 i+27}{25 + 81} = \frac{-8-78i }{106} = \frac{-4}{53} + \frac{-39}{53}i \)
6. \((9-10i) \cdot (-7+2i)= -63+18i +70 i-20i^2 = -63+18i +70 i+20= \color{red}{-63+20}\color{blue}{+18i +70i}=\color{red}{-43}\color{blue}{+88i}\)
7. \(\frac{-8-6i}{-2-2i}= \frac{-8-6i}{-2-2i} \cdot \frac{-2+2i}{-2+2i} = \frac{16-16i +12 i-12i^2 }{(-2)^2-(-2i)^2} = \frac{16-16i +12 i+12}{4 + 4} = \frac{28-4i }{8} = \frac{7}{2} + \frac{-1}{2}i \)
8. \((3+3i) \cdot (8-9i)= 24-27i +24 i-27i^2 = 24-27i +24 i+27= \color{red}{24+27}\color{blue}{-27i +24i}=\color{red}{51}\color{blue}{-3i}\)
9. \((5-6i)\cdot (-6i)= -30 i+36i^2 = \color{red}{-36}\color{blue}{-30i}\)
10. \((6+6i)+(-10-5i)= 6+6i -10-5i =\color{red}{6-10}\color{blue}{+6i -5i}=\color{red}{-4}\color{blue}{+i}\)
11. \(\frac{-10-3i}{5-3i}= \frac{-10-3i}{5-3i} \cdot \frac{5+3i}{5+3i} = \frac{-50-30i -15 i-9i^2 }{(5)^2-(-3i)^2} = \frac{-50-30i -15 i+9}{25 + 9} = \frac{-41-45i }{34} = \frac{-41}{34} + \frac{-45}{34}i \)
12. \((4+8i)-(-6+4i)= 4+8i +6-4i =\color{red}{4+6}\color{blue}{+8i -4i}=\color{red}{10}\color{blue}{+4i}\)