Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-3+3i)+(-6+2i)= -3+3i -6+2i =\color{red}{-3-6}\color{blue}{+3i +2i}=\color{red}{-9}\color{blue}{+5i}\)
2. \(\frac{-2+8i}{4-7i}= \frac{-2+8i}{4-7i} \cdot \frac{4+7i}{4+7i} = \frac{-8-14i +32 i+56i^2 }{(4)^2-(-7i)^2} = \frac{-8-14i +32 i-56}{16 + 49} = \frac{-64+18i }{65} = \frac{-64}{65} - \frac{-18}{65}i \)
3. \((-9-2i) \cdot (1-6i)= -9+54i -2 i+12i^2 = -9+54i -2 i-12= \color{red}{-9-12}\color{blue}{+54i -2i}=\color{red}{-21}\color{blue}{+52i}\)
4. \((-2-6i) \cdot (-2+7i)= 4-14i +12 i-42i^2 = 4-14i +12 i+42= \color{red}{4+42}\color{blue}{-14i +12i}=\color{red}{46}\color{blue}{-2i}\)
5. \((-3+10i)+(-6-10i)= -3+10i -6-10i =\color{red}{-3-6}\color{blue}{+10i -10i}=\color{red}{-9}\)
6. \((2-7i)\cdot (-i)= -2 i+7i^2 = \color{red}{-7}\color{blue}{-2i}\)
7. \(\frac{-8-i}{-10-10i}= \frac{-8-i}{-10-10i} \cdot \frac{-10+10i}{-10+10i} = \frac{80-80i +10 i-10i^2 }{(-10)^2-(-10i)^2} = \frac{80-80i +10 i+10}{100 + 100} = \frac{90-70i }{200} = \frac{9}{20} + \frac{-7}{20}i \)
8. \((-2+3i) \cdot (6+7i)= -12-14i +18 i+21i^2 = -12-14i +18 i-21= \color{red}{-12-21}\color{blue}{-14i +18i}=\color{red}{-33}\color{blue}{+4i}\)
9. \(\frac{-5-2i}{-3-2i}= \frac{-5-2i}{-3-2i} \cdot \frac{-3+2i}{-3+2i} = \frac{15-10i +6 i-4i^2 }{(-3)^2-(-2i)^2} = \frac{15-10i +6 i+4}{9 + 4} = \frac{19-4i }{13} = \frac{19}{13} + \frac{-4}{13}i \)
10. \((4-4i)-(8-6i)= 4-4i -8+6i =\color{red}{4-8}\color{blue}{-4i +6i}=\color{red}{-4}\color{blue}{+2i}\)
11. \((-8i) \cdot (-9+3i)= +72 i-24i^2 = \color{red}{24}\color{blue}{+72i}\)
12. \(\frac{3-8i}{-4+5i}= \frac{3-8i}{-4+5i} \cdot \frac{-4-5i}{-4-5i} = \frac{-12-15i +32 i+40i^2 }{(-4)^2-(5i)^2} = \frac{-12-15i +32 i-40}{16 + 25} = \frac{-52+17i }{41} = \frac{-52}{41} - \frac{-17}{41}i \)