Basisbewerkingen gemengd (a+bi)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(\frac{-8-2i}{4-10i}= \frac{-8-2i}{4-10i} \cdot \frac{4+10i}{4+10i} = \frac{-32-80i -8 i-20i^2 }{(4)^2-(-10i)^2} = \frac{-32-80i -8 i+20}{16 + 100} = \frac{-12-88i }{116} = \frac{-3}{29} + \frac{-22}{29}i \)
2. \((-9i) \cdot (-7+10i)= +63 i-90i^2 = \color{red}{90}\color{blue}{+63i}\)
3. \((-3+6i)-(6+10i)= -3+6i -6-10i =\color{red}{-3-6}\color{blue}{+6i -10i}=\color{red}{-9}\color{blue}{-4i}\)
4. \((-4-4i) \cdot (-2-6i)= 8+24i +8 i+24i^2 = 8+24i +8 i-24= \color{red}{8-24}\color{blue}{+24i +8i}=\color{red}{-16}\color{blue}{+32i}\)
5. \((6-8i)-(9-10i)= 6-8i -9+10i =\color{red}{6-9}\color{blue}{-8i +10i}=\color{red}{-3}\color{blue}{+2i}\)
6. \((+8i) \cdot (-4+10i)= -32 i+80i^2 = \color{red}{-80}\color{blue}{-32i}\)
7. \(\frac{9+3i}{-8-7i}= \frac{9+3i}{-8-7i} \cdot \frac{-8+7i}{-8+7i} = \frac{-72+63i -24 i+21i^2 }{(-8)^2-(-7i)^2} = \frac{-72+63i -24 i-21}{64 + 49} = \frac{-93+39i }{113} = \frac{-93}{113} - \frac{-39}{113}i \)
8. \(\frac{2+i}{9-3i}= \frac{2+i}{9-3i} \cdot \frac{9+3i}{9+3i} = \frac{18+6i +9 i+3i^2 }{(9)^2-(-3i)^2} = \frac{18+6i +9 i-3}{81 + 9} = \frac{15+15i }{90} = \frac{1}{6} - \frac{-1}{6}i \)
9. \((-2-10i) \cdot (-8-9i)= 16+18i +80 i+90i^2 = 16+18i +80 i-90= \color{red}{16-90}\color{blue}{+18i +80i}=\color{red}{-74}\color{blue}{+98i}\)
10. \((-4+8i)\cdot (-7i)= +28 i-56i^2 = \color{red}{56}\color{blue}{+28i}\)
11. \(\frac{-6-10i}{3-2i}= \frac{-6-10i}{3-2i} \cdot \frac{3+2i}{3+2i} = \frac{-18-12i -30 i-20i^2 }{(3)^2-(-2i)^2} = \frac{-18-12i -30 i+20}{9 + 4} = \frac{2-42i }{13} = \frac{2}{13} + \frac{-42}{13}i \)
12. \((-1-8i) \cdot (-6-9i)= 6+9i +48 i+72i^2 = 6+9i +48 i-72= \color{red}{6-72}\color{blue}{+9i +48i}=\color{red}{-66}\color{blue}{+57i}\)