Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((7-6i)\cdot (-i)= -7 i+6i^2 = \color{red}{-6}\color{blue}{-7i}\)
2. \((8-6i) \cdot (2-3i)= 16-24i -12 i+18i^2 = 16-24i -12 i-18= \color{red}{16-18}\color{blue}{-24i -12i}=\color{red}{-2}\color{blue}{-36i}\)
3. \(\frac{10-5i}{-8-6i}= \frac{10-5i}{-8-6i} \cdot \frac{-8+6i}{-8+6i} = \frac{-80+60i +40 i-30i^2 }{(-8)^2-(-6i)^2} = \frac{-80+60i +40 i+30}{64 + 36} = \frac{-50+100i }{100} = \frac{-1}{2} - -1i\)
4. \(\frac{4+7i}{-8+4i}= \frac{4+7i}{-8+4i} \cdot \frac{-8-4i}{-8-4i} = \frac{-32-16i -56 i-28i^2 }{(-8)^2-(4i)^2} = \frac{-32-16i -56 i+28}{64 + 16} = \frac{-4-72i }{80} = \frac{-1}{20} + \frac{-9}{10}i \)
5. \((5-4i)\cdot (+5i)= +25 i-20i^2 = \color{red}{20}\color{blue}{+25i}\)
6. \((-2i) \cdot (7+2i)= -14 i-4i^2 = \color{red}{4}\color{blue}{-14i}\)
7. \((3-10i) \cdot (-3-7i)= -9-21i +30 i+70i^2 = -9-21i +30 i-70= \color{red}{-9-70}\color{blue}{-21i +30i}=\color{red}{-79}\color{blue}{+9i}\)
8. \(\frac{7-i}{-3+i}= \frac{7-i}{-3+i} \cdot \frac{-3-i}{-3-i} = \frac{-21-7i +3 i+i^2 }{(-3)^2-(1i)^2} = \frac{-21-7i +3 i-}{9 + 1} = \frac{-22-4i }{10} = \frac{-11}{5} + \frac{-2}{5}i \)
9. \(\frac{-5+8i}{6-4i}= \frac{-5+8i}{6-4i} \cdot \frac{6+4i}{6+4i} = \frac{-30-20i +48 i+32i^2 }{(6)^2-(-4i)^2} = \frac{-30-20i +48 i-32}{36 + 16} = \frac{-62+28i }{52} = \frac{-31}{26} - \frac{-7}{13}i \)
10. \((-8-4i)\cdot (+3i)= -24 i-12i^2 = \color{red}{12}\color{blue}{-24i}\)
11. \((+5i) \cdot (-3+i)= -15 i+5i^2 = \color{red}{-5}\color{blue}{-15i}\)
12. \((5-5i)\cdot (-10i)= -50 i+50i^2 = \color{red}{-50}\color{blue}{-50i}\)