Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((+6i) \cdot (9+3i)= +54 i+18i^2 = \color{red}{-18}\color{blue}{+54i}\)
2. \((6+8i) \cdot (-2+3i)= -12+18i -16 i+24i^2 = -12+18i -16 i-24= \color{red}{-12-24}\color{blue}{+18i -16i}=\color{red}{-36}\color{blue}{+2i}\)
3. \(\frac{-1-7i}{-8-8i}= \frac{-1-7i}{-8-8i} \cdot \frac{-8+8i}{-8+8i} = \frac{8-8i +56 i-56i^2 }{(-8)^2-(-8i)^2} = \frac{8-8i +56 i+56}{64 + 64} = \frac{64+48i }{128} = \frac{1}{2} - \frac{-3}{8}i \)
4. \(\frac{1-2i}{4-9i}= \frac{1-2i}{4-9i} \cdot \frac{4+9i}{4+9i} = \frac{4+9i -8 i-18i^2 }{(4)^2-(-9i)^2} = \frac{4+9i -8 i+18}{16 + 81} = \frac{22+i }{97} = \frac{22}{97} - \frac{-1}{97}i \)
5. \(\frac{-5+6i}{-1-i}= \frac{-5+6i}{-1-i} \cdot \frac{-1+i}{-1+i} = \frac{5-5i -6 i+6i^2 }{(-1)^2-(-1i)^2} = \frac{5-5i -6 i-6}{1 + 1} = \frac{-1-11i }{2} = \frac{-1}{2} + \frac{-11}{2}i \)
6. \((2+2i) \cdot (-4+10i)= -8+20i -8 i+20i^2 = -8+20i -8 i-20= \color{red}{-8-20}\color{blue}{+20i -8i}=\color{red}{-28}\color{blue}{+12i}\)
7. \(\frac{-2+5i}{9+7i}= \frac{-2+5i}{9+7i} \cdot \frac{9-7i}{9-7i} = \frac{-18+14i +45 i-35i^2 }{(9)^2-(7i)^2} = \frac{-18+14i +45 i+35}{81 + 49} = \frac{17+59i }{130} = \frac{17}{130} - \frac{-59}{130}i \)
8. \((+9i) \cdot (9+6i)= +81 i+54i^2 = \color{red}{-54}\color{blue}{+81i}\)
9. \(\frac{-8+4i}{5-3i}= \frac{-8+4i}{5-3i} \cdot \frac{5+3i}{5+3i} = \frac{-40-24i +20 i+12i^2 }{(5)^2-(-3i)^2} = \frac{-40-24i +20 i-12}{25 + 9} = \frac{-52-4i }{34} = \frac{-26}{17} + \frac{-2}{17}i \)
10. \((-2+6i) \cdot (8-10i)= -16+20i +48 i-60i^2 = -16+20i +48 i+60= \color{red}{-16+60}\color{blue}{+20i +48i}=\color{red}{44}\color{blue}{+68i}\)
11. \((-8i) \cdot (-7+3i)= +56 i-24i^2 = \color{red}{24}\color{blue}{+56i}\)
12. \((-5i) \cdot (-7+6i)= +35 i-30i^2 = \color{red}{30}\color{blue}{+35i}\)