Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-1-i) \cdot (1+6i)= -1-6i -1 i-6i^2 = -1-6i -1 i+6= \color{red}{-1+6}\color{blue}{-6i -i}=\color{red}{5}\color{blue}{-7i}\)
2. \((3-6i) \cdot (9+10i)= 27+30i -54 i-60i^2 = 27+30i -54 i+60= \color{red}{27+60}\color{blue}{+30i -54i}=\color{red}{87}\color{blue}{-24i}\)
3. \((1+5i) \cdot (-1+4i)= -1+4i -5 i+20i^2 = -1+4i -5 i-20= \color{red}{-1-20}\color{blue}{+4i -5i}=\color{red}{-21}\color{blue}{-i}\)
4. \((-2i) \cdot (-9-6i)= +18 i+12i^2 = \color{red}{-12}\color{blue}{+18i}\)
5. \((-4+10i)\cdot (-4i)= +16 i-40i^2 = \color{red}{40}\color{blue}{+16i}\)
6. \(\frac{-5+8i}{5+7i}= \frac{-5+8i}{5+7i} \cdot \frac{5-7i}{5-7i} = \frac{-25+35i +40 i-56i^2 }{(5)^2-(7i)^2} = \frac{-25+35i +40 i+56}{25 + 49} = \frac{31+75i }{74} = \frac{31}{74} - \frac{-75}{74}i \)
7. \((-3i) \cdot (-9-5i)= +27 i+15i^2 = \color{red}{-15}\color{blue}{+27i}\)
8. \(\frac{9-6i}{-9-7i}= \frac{9-6i}{-9-7i} \cdot \frac{-9+7i}{-9+7i} = \frac{-81+63i +54 i-42i^2 }{(-9)^2-(-7i)^2} = \frac{-81+63i +54 i+42}{81 + 49} = \frac{-39+117i }{130} = \frac{-3}{10} - \frac{-9}{10}i \)
9. \((10-8i) \cdot (10+2i)= 100+20i -80 i-16i^2 = 100+20i -80 i+16= \color{red}{100+16}\color{blue}{+20i -80i}=\color{red}{116}\color{blue}{-60i}\)
10. \(\frac{10-6i}{-6+3i}= \frac{10-6i}{-6+3i} \cdot \frac{-6-3i}{-6-3i} = \frac{-60-30i +36 i+18i^2 }{(-6)^2-(3i)^2} = \frac{-60-30i +36 i-18}{36 + 9} = \frac{-78+6i }{45} = \frac{-26}{15} - \frac{-2}{15}i \)
11. \((-5i) \cdot (-2+6i)= +10 i-30i^2 = \color{red}{30}\color{blue}{+10i}\)
12. \((-3+7i) \cdot (-2+4i)= 6-12i -14 i+28i^2 = 6-12i -14 i-28= \color{red}{6-28}\color{blue}{-12i -14i}=\color{red}{-22}\color{blue}{-26i}\)