Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-7i) \cdot (7-5i)= -49 i+35i^2 = \color{red}{-35}\color{blue}{-49i}\)
2. \(\frac{5+4i}{-1-5i}= \frac{5+4i}{-1-5i} \cdot \frac{-1+5i}{-1+5i} = \frac{-5+25i -4 i+20i^2 }{(-1)^2-(-5i)^2} = \frac{-5+25i -4 i-20}{1 + 25} = \frac{-25+21i }{26} = \frac{-25}{26} - \frac{-21}{26}i \)
3. \(\frac{-1+2i}{-1-8i}= \frac{-1+2i}{-1-8i} \cdot \frac{-1+8i}{-1+8i} = \frac{1-8i -2 i+16i^2 }{(-1)^2-(-8i)^2} = \frac{1-8i -2 i-16}{1 + 64} = \frac{-15-10i }{65} = \frac{-3}{13} + \frac{-2}{13}i \)
4. \((2-6i) \cdot (3+3i)= 6+6i -18 i-18i^2 = 6+6i -18 i+18= \color{red}{6+18}\color{blue}{+6i -18i}=\color{red}{24}\color{blue}{-12i}\)
5. \(\frac{-3-2i}{-8-2i}= \frac{-3-2i}{-8-2i} \cdot \frac{-8+2i}{-8+2i} = \frac{24-6i +16 i-4i^2 }{(-8)^2-(-2i)^2} = \frac{24-6i +16 i+4}{64 + 4} = \frac{28+10i }{68} = \frac{7}{17} - \frac{-5}{34}i \)
6. \((2+10i)\cdot (-9i)= -18 i-90i^2 = \color{red}{90}\color{blue}{-18i}\)
7. \((-2+3i)\cdot (-i)= +2 i-3i^2 = \color{red}{3}\color{blue}{+2i}\)
8. \((-3i) \cdot (-1-3i)= +3 i+9i^2 = \color{red}{-9}\color{blue}{+3i}\)
9. \((-3+7i) \cdot (-7-5i)= 21+15i -49 i-35i^2 = 21+15i -49 i+35= \color{red}{21+35}\color{blue}{+15i -49i}=\color{red}{56}\color{blue}{-34i}\)
10. \((1+i) \cdot (-10+5i)= -10+5i -10 i+5i^2 = -10+5i -10 i-5= \color{red}{-10-5}\color{blue}{+5i -10i}=\color{red}{-15}\color{blue}{-5i}\)
11. \(\frac{4+10i}{8-5i}= \frac{4+10i}{8-5i} \cdot \frac{8+5i}{8+5i} = \frac{32+20i +80 i+50i^2 }{(8)^2-(-5i)^2} = \frac{32+20i +80 i-50}{64 + 25} = \frac{-18+100i }{89} = \frac{-18}{89} - \frac{-100}{89}i \)
12. \(\frac{8+i}{-2+5i}= \frac{8+i}{-2+5i} \cdot \frac{-2-5i}{-2-5i} = \frac{-16-40i -2 i-5i^2 }{(-2)^2-(5i)^2} = \frac{-16-40i -2 i+5}{4 + 25} = \frac{-11-42i }{29} = \frac{-11}{29} + \frac{-42}{29}i \)