Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \(\frac{3+3i}{-3+8i}= \frac{3+3i}{-3+8i} \cdot \frac{-3-8i}{-3-8i} = \frac{-9-24i -9 i-24i^2 }{(-3)^2-(8i)^2} = \frac{-9-24i -9 i+24}{9 + 64} = \frac{15-33i }{73} = \frac{15}{73} + \frac{-33}{73}i \)
2. \((7+4i) \cdot (-7+i)= -49+7i -28 i+4i^2 = -49+7i -28 i-4= \color{red}{-49-4}\color{blue}{+7i -28i}=\color{red}{-53}\color{blue}{-21i}\)
3. \((-3-9i) \cdot (-5-4i)= 15+12i +45 i+36i^2 = 15+12i +45 i-36= \color{red}{15-36}\color{blue}{+12i +45i}=\color{red}{-21}\color{blue}{+57i}\)
4. \(\frac{3+6i}{-1+8i}= \frac{3+6i}{-1+8i} \cdot \frac{-1-8i}{-1-8i} = \frac{-3-24i -6 i-48i^2 }{(-1)^2-(8i)^2} = \frac{-3-24i -6 i+48}{1 + 64} = \frac{45-30i }{65} = \frac{9}{13} + \frac{-6}{13}i \)
5. \((-6-6i) \cdot (-5-7i)= 30+42i +30 i+42i^2 = 30+42i +30 i-42= \color{red}{30-42}\color{blue}{+42i +30i}=\color{red}{-12}\color{blue}{+72i}\)
6. \(\frac{-2-2i}{-8-7i}= \frac{-2-2i}{-8-7i} \cdot \frac{-8+7i}{-8+7i} = \frac{16-14i +16 i-14i^2 }{(-8)^2-(-7i)^2} = \frac{16-14i +16 i+14}{64 + 49} = \frac{30+2i }{113} = \frac{30}{113} - \frac{-2}{113}i \)
7. \(\frac{2-8i}{1+5i}= \frac{2-8i}{1+5i} \cdot \frac{1-5i}{1-5i} = \frac{2-10i -8 i+40i^2 }{(1)^2-(5i)^2} = \frac{2-10i -8 i-40}{1 + 25} = \frac{-38-18i }{26} = \frac{-19}{13} + \frac{-9}{13}i \)
8. \(\frac{-2-3i}{-9+6i}= \frac{-2-3i}{-9+6i} \cdot \frac{-9-6i}{-9-6i} = \frac{18+12i +27 i+18i^2 }{(-9)^2-(6i)^2} = \frac{18+12i +27 i-18}{81 + 36} = \frac{0+39i }{117} = 0- \frac{-1}{3}i \)
9. \((-2i) \cdot (3+5i)= -6 i-10i^2 = \color{red}{10}\color{blue}{-6i}\)
10. \((-7i) \cdot (-7-2i)= +49 i+14i^2 = \color{red}{-14}\color{blue}{+49i}\)
11. \((-i) \cdot (6-7i)= -6 i+7i^2 = \color{red}{-7}\color{blue}{-6i}\)
12. \((-4+10i) \cdot (-5+9i)= 20-36i -50 i+90i^2 = 20-36i -50 i-90= \color{red}{20-90}\color{blue}{-36i -50i}=\color{red}{-70}\color{blue}{-86i}\)