Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \(\frac{-4+10i}{-6+3i}= \frac{-4+10i}{-6+3i} \cdot \frac{-6-3i}{-6-3i} = \frac{24+12i -60 i-30i^2 }{(-6)^2-(3i)^2} = \frac{24+12i -60 i+30}{36 + 9} = \frac{54-48i }{45} = \frac{6}{5} + \frac{-16}{15}i \)
2. \((8+8i)\cdot (+4i)= +32 i+32i^2 = \color{red}{-32}\color{blue}{+32i}\)
3. \((10+2i)\cdot (+i)= +10 i+2i^2 = \color{red}{-2}\color{blue}{+10i}\)
4. \((3-7i) \cdot (10-7i)= 30-21i -70 i+49i^2 = 30-21i -70 i-49= \color{red}{30-49}\color{blue}{-21i -70i}=\color{red}{-19}\color{blue}{-91i}\)
5. \((1-7i) \cdot (-2+i)= -2+i +14 i-7i^2 = -2+i +14 i+7= \color{red}{-2+7}\color{blue}{+i +14i}=\color{red}{5}\color{blue}{+15i}\)
6. \((7-5i) \cdot (9-8i)= 63-56i -45 i+40i^2 = 63-56i -45 i-40= \color{red}{63-40}\color{blue}{-56i -45i}=\color{red}{23}\color{blue}{-101i}\)
7. \((7+4i) \cdot (10+10i)= 70+70i +40 i+40i^2 = 70+70i +40 i-40= \color{red}{70-40}\color{blue}{+70i +40i}=\color{red}{30}\color{blue}{+110i}\)
8. \(\frac{-4-3i}{2-6i}= \frac{-4-3i}{2-6i} \cdot \frac{2+6i}{2+6i} = \frac{-8-24i -6 i-18i^2 }{(2)^2-(-6i)^2} = \frac{-8-24i -6 i+18}{4 + 36} = \frac{10-30i }{40} = \frac{1}{4} + \frac{-3}{4}i \)
9. \((-10i) \cdot (2-4i)= -20 i+40i^2 = \color{red}{-40}\color{blue}{-20i}\)
10. \(\frac{7+6i}{10-7i}= \frac{7+6i}{10-7i} \cdot \frac{10+7i}{10+7i} = \frac{70+49i +60 i+42i^2 }{(10)^2-(-7i)^2} = \frac{70+49i +60 i-42}{100 + 49} = \frac{28+109i }{149} = \frac{28}{149} - \frac{-109}{149}i \)
11. \(\frac{9-5i}{4-5i}= \frac{9-5i}{4-5i} \cdot \frac{4+5i}{4+5i} = \frac{36+45i -20 i-25i^2 }{(4)^2-(-5i)^2} = \frac{36+45i -20 i+25}{16 + 25} = \frac{61+25i }{41} = \frac{61}{41} - \frac{-25}{41}i \)
12. \((9+10i) \cdot (-2-2i)= -18-18i -20 i-20i^2 = -18-18i -20 i+20= \color{red}{-18+20}\color{blue}{-18i -20i}=\color{red}{2}\color{blue}{-38i}\)