Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((8-9i) \cdot (-1-6i)= -8-48i +9 i+54i^2 = -8-48i +9 i-54= \color{red}{-8-54}\color{blue}{-48i +9i}=\color{red}{-62}\color{blue}{-39i}\)
2. \((8-8i)\cdot (-10i)= -80 i+80i^2 = \color{red}{-80}\color{blue}{-80i}\)
3. \(\frac{9-4i}{-9-10i}= \frac{9-4i}{-9-10i} \cdot \frac{-9+10i}{-9+10i} = \frac{-81+90i +36 i-40i^2 }{(-9)^2-(-10i)^2} = \frac{-81+90i +36 i+40}{81 + 100} = \frac{-41+126i }{181} = \frac{-41}{181} - \frac{-126}{181}i \)
4. \((-9+4i) \cdot (8+10i)= -72-90i +32 i+40i^2 = -72-90i +32 i-40= \color{red}{-72-40}\color{blue}{-90i +32i}=\color{red}{-112}\color{blue}{-58i}\)
5. \((4+9i) \cdot (2-i)= 8-4i +18 i-9i^2 = 8-4i +18 i+9= \color{red}{8+9}\color{blue}{-4i +18i}=\color{red}{17}\color{blue}{+14i}\)
6. \((10-2i) \cdot (1-7i)= 10-70i -2 i+14i^2 = 10-70i -2 i-14= \color{red}{10-14}\color{blue}{-70i -2i}=\color{red}{-4}\color{blue}{-72i}\)
7. \(\frac{9+9i}{-10+7i}= \frac{9+9i}{-10+7i} \cdot \frac{-10-7i}{-10-7i} = \frac{-90-63i -90 i-63i^2 }{(-10)^2-(7i)^2} = \frac{-90-63i -90 i+63}{100 + 49} = \frac{-27-153i }{149} = \frac{-27}{149} + \frac{-153}{149}i \)
8. \((6-4i) \cdot (-6+7i)= -36+42i +24 i-28i^2 = -36+42i +24 i+28= \color{red}{-36+28}\color{blue}{+42i +24i}=\color{red}{-8}\color{blue}{+66i}\)
9. \(\frac{3+7i}{3+8i}= \frac{3+7i}{3+8i} \cdot \frac{3-8i}{3-8i} = \frac{9-24i +21 i-56i^2 }{(3)^2-(8i)^2} = \frac{9-24i +21 i+56}{9 + 64} = \frac{65-3i }{73} = \frac{65}{73} + \frac{-3}{73}i \)
10. \((10+6i) \cdot (-6-5i)= -60-50i -36 i-30i^2 = -60-50i -36 i+30= \color{red}{-60+30}\color{blue}{-50i -36i}=\color{red}{-30}\color{blue}{-86i}\)
11. \((-1-5i) \cdot (-4-i)= 4+i +20 i+5i^2 = 4+i +20 i-5= \color{red}{4-5}\color{blue}{+i +20i}=\color{red}{-1}\color{blue}{+21i}\)
12. \((-1+8i)\cdot (-9i)= +9 i-72i^2 = \color{red}{72}\color{blue}{+9i}\)