Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((5-2i) \cdot (9-6i)= 45-30i -18 i+12i^2 = 45-30i -18 i-12= \color{red}{45-12}\color{blue}{-30i -18i}=\color{red}{33}\color{blue}{-48i}\)
2. \((1+i) \cdot (-8-8i)= -8-8i -8 i-8i^2 = -8-8i -8 i+8= \color{red}{-8+8}\color{blue}{-8i -8i}=\color{blue}{-16i}\)
3. \(\frac{8-2i}{10+i}= \frac{8-2i}{10+i} \cdot \frac{10-i}{10-i} = \frac{80-8i -20 i+2i^2 }{(10)^2-(1i)^2} = \frac{80-8i -20 i-2}{100 + 1} = \frac{78-28i }{101} = \frac{78}{101} + \frac{-28}{101}i \)
4. \(\frac{-2+8i}{8+4i}= \frac{-2+8i}{8+4i} \cdot \frac{8-4i}{8-4i} = \frac{-16+8i +64 i-32i^2 }{(8)^2-(4i)^2} = \frac{-16+8i +64 i+32}{64 + 16} = \frac{16+72i }{80} = \frac{1}{5} - \frac{-9}{10}i \)
5. \((2+8i) \cdot (-9-7i)= -18-14i -72 i-56i^2 = -18-14i -72 i+56= \color{red}{-18+56}\color{blue}{-14i -72i}=\color{red}{38}\color{blue}{-86i}\)
6. \((-3i) \cdot (-10+6i)= +30 i-18i^2 = \color{red}{18}\color{blue}{+30i}\)
7. \((-2+6i) \cdot (7-9i)= -14+18i +42 i-54i^2 = -14+18i +42 i+54= \color{red}{-14+54}\color{blue}{+18i +42i}=\color{red}{40}\color{blue}{+60i}\)
8. \((-8+5i) \cdot (-3-9i)= 24+72i -15 i-45i^2 = 24+72i -15 i+45= \color{red}{24+45}\color{blue}{+72i -15i}=\color{red}{69}\color{blue}{+57i}\)
9. \(\frac{-7+9i}{5+2i}= \frac{-7+9i}{5+2i} \cdot \frac{5-2i}{5-2i} = \frac{-35+14i +45 i-18i^2 }{(5)^2-(2i)^2} = \frac{-35+14i +45 i+18}{25 + 4} = \frac{-17+59i }{29} = \frac{-17}{29} - \frac{-59}{29}i \)
10. \((7-7i)\cdot (+2i)= +14 i-14i^2 = \color{red}{14}\color{blue}{+14i}\)
11. \((2-3i)\cdot (+7i)= +14 i-21i^2 = \color{red}{21}\color{blue}{+14i}\)
12. \((-1-5i)\cdot (-6i)= +6 i+30i^2 = \color{red}{-30}\color{blue}{+6i}\)