Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-6-8i)\cdot (-4i)= +24 i+32i^2 = \color{red}{-32}\color{blue}{+24i}\)
2. \((-10-2i) \cdot (5-9i)= -50+90i -10 i+18i^2 = -50+90i -10 i-18= \color{red}{-50-18}\color{blue}{+90i -10i}=\color{red}{-68}\color{blue}{+80i}\)
3. \((-4-2i)\cdot (-i)= +4 i+2i^2 = \color{red}{-2}\color{blue}{+4i}\)
4. \((5-4i) \cdot (2-9i)= 10-45i -8 i+36i^2 = 10-45i -8 i-36= \color{red}{10-36}\color{blue}{-45i -8i}=\color{red}{-26}\color{blue}{-53i}\)
5. \((-3-5i) \cdot (9+10i)= -27-30i -45 i-50i^2 = -27-30i -45 i+50= \color{red}{-27+50}\color{blue}{-30i -45i}=\color{red}{23}\color{blue}{-75i}\)
6. \((-10+4i) \cdot (6-6i)= -60+60i +24 i-24i^2 = -60+60i +24 i+24= \color{red}{-60+24}\color{blue}{+60i +24i}=\color{red}{-36}\color{blue}{+84i}\)
7. \((+4i) \cdot (8+10i)= +32 i+40i^2 = \color{red}{-40}\color{blue}{+32i}\)
8. \((7+9i) \cdot (4-9i)= 28-63i +36 i-81i^2 = 28-63i +36 i+81= \color{red}{28+81}\color{blue}{-63i +36i}=\color{red}{109}\color{blue}{-27i}\)
9. \(\frac{-1+7i}{-7-10i}= \frac{-1+7i}{-7-10i} \cdot \frac{-7+10i}{-7+10i} = \frac{7-10i -49 i+70i^2 }{(-7)^2-(-10i)^2} = \frac{7-10i -49 i-70}{49 + 100} = \frac{-63-59i }{149} = \frac{-63}{149} + \frac{-59}{149}i \)
10. \(\frac{-4-7i}{-4+4i}= \frac{-4-7i}{-4+4i} \cdot \frac{-4-4i}{-4-4i} = \frac{16+16i +28 i+28i^2 }{(-4)^2-(4i)^2} = \frac{16+16i +28 i-28}{16 + 16} = \frac{-12+44i }{32} = \frac{-3}{8} - \frac{-11}{8}i \)
11. \(\frac{4-5i}{5-7i}= \frac{4-5i}{5-7i} \cdot \frac{5+7i}{5+7i} = \frac{20+28i -25 i-35i^2 }{(5)^2-(-7i)^2} = \frac{20+28i -25 i+35}{25 + 49} = \frac{55+3i }{74} = \frac{55}{74} - \frac{-3}{74}i \)
12. \((-3i) \cdot (8-7i)= -24 i+21i^2 = \color{red}{-21}\color{blue}{-24i}\)