Basisbewerkingen gemengd (a+bi)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \((+4i) \cdot (-4-10i)= -16 i-40i^2 = \color{red}{40}\color{blue}{-16i}\)
2. \(\frac{-3+i}{-9-7i}= \frac{-3+i}{-9-7i} \cdot \frac{-9+7i}{-9+7i} = \frac{27-21i -9 i+7i^2 }{(-9)^2-(-7i)^2} = \frac{27-21i -9 i-7}{81 + 49} = \frac{20-30i }{130} = \frac{2}{13} + \frac{-3}{13}i \)
3. \(\frac{7+i}{6-9i}= \frac{7+i}{6-9i} \cdot \frac{6+9i}{6+9i} = \frac{42+63i +6 i+9i^2 }{(6)^2-(-9i)^2} = \frac{42+63i +6 i-9}{36 + 81} = \frac{33+69i }{117} = \frac{11}{39} - \frac{-23}{39}i \)
4. \((-3-7i) \cdot (2+4i)= -6-12i -14 i-28i^2 = -6-12i -14 i+28= \color{red}{-6+28}\color{blue}{-12i -14i}=\color{red}{22}\color{blue}{-26i}\)
5. \((-7-7i) \cdot (2+9i)= -14-63i -14 i-63i^2 = -14-63i -14 i+63= \color{red}{-14+63}\color{blue}{-63i -14i}=\color{red}{49}\color{blue}{-77i}\)
6. \((8+4i)+(7-5i)= 8+4i +7-5i =\color{red}{8+7}\color{blue}{+4i -5i}=\color{red}{15}\color{blue}{-i}\)
7. \((8-6i) \cdot (9-2i)= 72-16i -54 i+12i^2 = 72-16i -54 i-12= \color{red}{72-12}\color{blue}{-16i -54i}=\color{red}{60}\color{blue}{-70i}\)
8. \((-4+7i) \cdot (-7+i)= 28-4i -49 i+7i^2 = 28-4i -49 i-7= \color{red}{28-7}\color{blue}{-4i -49i}=\color{red}{21}\color{blue}{-53i}\)
9. \((-7-7i)+(-7+3i)= -7-7i -7+3i =\color{red}{-7-7}\color{blue}{-7i +3i}=\color{red}{-14}\color{blue}{-4i}\)
10. \((-9+6i)-(-7-4i)= -9+6i +7+4i =\color{red}{-9+7}\color{blue}{+6i +4i}=\color{red}{-2}\color{blue}{+10i}\)
11. \((-10i) \cdot (-7-4i)= +70 i+40i^2 = \color{red}{-40}\color{blue}{+70i}\)
12. \((3-i) \cdot (9+8i)= 27+24i -9 i-8i^2 = 27+24i -9 i+8= \color{red}{27+8}\color{blue}{+24i -9i}=\color{red}{35}\color{blue}{+15i}\)