Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-5-10i) \cdot (10-2i)= -50+10i -100 i+20i^2 = -50+10i -100 i-20= \color{red}{-50-20}\color{blue}{+10i -100i}=\color{red}{-70}\color{blue}{-90i}\)
2. \((2-8i)\cdot (-5i)= -10 i+40i^2 = \color{red}{-40}\color{blue}{-10i}\)
3. \((6-5i)\cdot (-10i)= -60 i+50i^2 = \color{red}{-50}\color{blue}{-60i}\)
4. \((-2i) \cdot (-2-5i)= +4 i+10i^2 = \color{red}{-10}\color{blue}{+4i}\)
5. \((-1-2i) \cdot (9-8i)= -9+8i -18 i+16i^2 = -9+8i -18 i-16= \color{red}{-9-16}\color{blue}{+8i -18i}=\color{red}{-25}\color{blue}{-10i}\)
6. \((-2i) \cdot (-8+7i)= +16 i-14i^2 = \color{red}{14}\color{blue}{+16i}\)
7. \(\frac{-10+8i}{10+2i}= \frac{-10+8i}{10+2i} \cdot \frac{10-2i}{10-2i} = \frac{-100+20i +80 i-16i^2 }{(10)^2-(2i)^2} = \frac{-100+20i +80 i+16}{100 + 4} = \frac{-84+100i }{104} = \frac{-21}{26} - \frac{-25}{26}i \)
8. \((-4-4i) \cdot (5+10i)= -20-40i -20 i-40i^2 = -20-40i -20 i+40= \color{red}{-20+40}\color{blue}{-40i -20i}=\color{red}{20}\color{blue}{-60i}\)
9. \((4+9i) \cdot (1-10i)= 4-40i +9 i-90i^2 = 4-40i +9 i+90= \color{red}{4+90}\color{blue}{-40i +9i}=\color{red}{94}\color{blue}{-31i}\)
10. \(\frac{-3+4i}{-6-10i}= \frac{-3+4i}{-6-10i} \cdot \frac{-6+10i}{-6+10i} = \frac{18-30i -24 i+40i^2 }{(-6)^2-(-10i)^2} = \frac{18-30i -24 i-40}{36 + 100} = \frac{-22-54i }{136} = \frac{-11}{68} + \frac{-27}{68}i \)
11. \(\frac{5-10i}{10+9i}= \frac{5-10i}{10+9i} \cdot \frac{10-9i}{10-9i} = \frac{50-45i -100 i+90i^2 }{(10)^2-(9i)^2} = \frac{50-45i -100 i-90}{100 + 81} = \frac{-40-145i }{181} = \frac{-40}{181} + \frac{-145}{181}i \)
12. \(\frac{-1+4i}{-10+i}= \frac{-1+4i}{-10+i} \cdot \frac{-10-i}{-10-i} = \frac{10+i -40 i-4i^2 }{(-10)^2-(1i)^2} = \frac{10+i -40 i+4}{100 + 1} = \frac{14-39i }{101} = \frac{14}{101} + \frac{-39}{101}i \)