Vermenigvuldigen en delen (a+bi)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \((-i) \cdot (7+10i)= -7 i-10i^2 = \color{red}{10}\color{blue}{-7i}\)
2. \(\frac{-9-10i}{-3-6i}= \frac{-9-10i}{-3-6i} \cdot \frac{-3+6i}{-3+6i} = \frac{27-54i +30 i-60i^2 }{(-3)^2-(-6i)^2} = \frac{27-54i +30 i+60}{9 + 36} = \frac{87-24i }{45} = \frac{29}{15} + \frac{-8}{15}i \)
3. \((+3i) \cdot (-9-i)= -27 i-3i^2 = \color{red}{3}\color{blue}{-27i}\)
4. \((-9+7i)\cdot (+10i)= -90 i+70i^2 = \color{red}{-70}\color{blue}{-90i}\)
5. \((+4i) \cdot (7+2i)= +28 i+8i^2 = \color{red}{-8}\color{blue}{+28i}\)
6. \((-2+i)\cdot (+7i)= -14 i+7i^2 = \color{red}{-7}\color{blue}{-14i}\)
7. \(\frac{3+4i}{6-8i}= \frac{3+4i}{6-8i} \cdot \frac{6+8i}{6+8i} = \frac{18+24i +24 i+32i^2 }{(6)^2-(-8i)^2} = \frac{18+24i +24 i-32}{36 + 64} = \frac{-14+48i }{100} = \frac{-7}{50} - \frac{-12}{25}i \)
8. \((-8-3i) \cdot (-3+2i)= 24-16i +9 i-6i^2 = 24-16i +9 i+6= \color{red}{24+6}\color{blue}{-16i +9i}=\color{red}{30}\color{blue}{-7i}\)
9. \((-4+3i)\cdot (-6i)= +24 i-18i^2 = \color{red}{18}\color{blue}{+24i}\)
10. \(\frac{10+8i}{-10-6i}= \frac{10+8i}{-10-6i} \cdot \frac{-10+6i}{-10+6i} = \frac{-100+60i -80 i+48i^2 }{(-10)^2-(-6i)^2} = \frac{-100+60i -80 i-48}{100 + 36} = \frac{-148-20i }{136} = \frac{-37}{34} + \frac{-5}{34}i \)
11. \((10-9i) \cdot (-7-6i)= -70-60i +63 i+54i^2 = -70-60i +63 i-54= \color{red}{-70-54}\color{blue}{-60i +63i}=\color{red}{-124}\color{blue}{+3i}\)
12. \((-3i) \cdot (1+10i)= -3 i-30i^2 = \color{red}{30}\color{blue}{-3i}\)