Vermenigvuldigen en delen (a+bi)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \((-5+8i)\cdot (+i)= -5 i+8i^2 = \color{red}{-8}\color{blue}{-5i}\)
2. \(\frac{-10-3i}{8-6i}= \frac{-10-3i}{8-6i} \cdot \frac{8+6i}{8+6i} = \frac{-80-60i -24 i-18i^2 }{(8)^2-(-6i)^2} = \frac{-80-60i -24 i+18}{64 + 36} = \frac{-62-84i }{100} = \frac{-31}{50} + \frac{-21}{25}i \)
3. \((-4i) \cdot (-7+10i)= +28 i-40i^2 = \color{red}{40}\color{blue}{+28i}\)
4. \((7-10i) \cdot (4-8i)= 28-56i -40 i+80i^2 = 28-56i -40 i-80= \color{red}{28-80}\color{blue}{-56i -40i}=\color{red}{-52}\color{blue}{-96i}\)
5. \((-1+8i) \cdot (-7+10i)= 7-10i -56 i+80i^2 = 7-10i -56 i-80= \color{red}{7-80}\color{blue}{-10i -56i}=\color{red}{-73}\color{blue}{-66i}\)
6. \(\frac{2-7i}{-7+2i}= \frac{2-7i}{-7+2i} \cdot \frac{-7-2i}{-7-2i} = \frac{-14-4i +49 i+14i^2 }{(-7)^2-(2i)^2} = \frac{-14-4i +49 i-14}{49 + 4} = \frac{-28+45i }{53} = \frac{-28}{53} - \frac{-45}{53}i \)
7. \(\frac{3+7i}{-2-9i}= \frac{3+7i}{-2-9i} \cdot \frac{-2+9i}{-2+9i} = \frac{-6+27i -14 i+63i^2 }{(-2)^2-(-9i)^2} = \frac{-6+27i -14 i-63}{4 + 81} = \frac{-69+13i }{85} = \frac{-69}{85} - \frac{-13}{85}i \)
8. \((4+8i)\cdot (-2i)= -8 i-16i^2 = \color{red}{16}\color{blue}{-8i}\)
9. \((-5-5i) \cdot (8-i)= -40+5i -40 i+5i^2 = -40+5i -40 i-5= \color{red}{-40-5}\color{blue}{+5i -40i}=\color{red}{-45}\color{blue}{-35i}\)
10. \((-2+7i)\cdot (+7i)= -14 i+49i^2 = \color{red}{-49}\color{blue}{-14i}\)
11. \(\frac{1-2i}{-2+8i}= \frac{1-2i}{-2+8i} \cdot \frac{-2-8i}{-2-8i} = \frac{-2-8i +4 i+16i^2 }{(-2)^2-(8i)^2} = \frac{-2-8i +4 i-16}{4 + 64} = \frac{-18-4i }{68} = \frac{-9}{34} + \frac{-1}{17}i \)
12. \(\frac{3-4i}{-9-2i}= \frac{3-4i}{-9-2i} \cdot \frac{-9+2i}{-9+2i} = \frac{-27+6i +36 i-8i^2 }{(-9)^2-(-2i)^2} = \frac{-27+6i +36 i+8}{81 + 4} = \frac{-19+42i }{85} = \frac{-19}{85} - \frac{-42}{85}i \)