Basisbewerkingen gemengd (a+bi)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(\frac{-4-2i}{-8-10i}= \frac{-4-2i}{-8-10i} \cdot \frac{-8+10i}{-8+10i} = \frac{32-40i +16 i-20i^2 }{(-8)^2-(-10i)^2} = \frac{32-40i +16 i+20}{64 + 100} = \frac{52-24i }{164} = \frac{13}{41} + \frac{-6}{41}i \)
2. \((-8-i)\cdot (-8i)= +64 i+8i^2 = \color{red}{-8}\color{blue}{+64i}\)
3. \(\frac{-3-6i}{8+9i}= \frac{-3-6i}{8+9i} \cdot \frac{8-9i}{8-9i} = \frac{-24+27i -48 i+54i^2 }{(8)^2-(9i)^2} = \frac{-24+27i -48 i-54}{64 + 81} = \frac{-78-21i }{145} = \frac{-78}{145} + \frac{-21}{145}i \)
4. \(\frac{-2+10i}{-7+2i}= \frac{-2+10i}{-7+2i} \cdot \frac{-7-2i}{-7-2i} = \frac{14+4i -70 i-20i^2 }{(-7)^2-(2i)^2} = \frac{14+4i -70 i+20}{49 + 4} = \frac{34-66i }{53} = \frac{34}{53} + \frac{-66}{53}i \)
5. \((-9-2i)+(2-10i)= -9-2i +2-10i =\color{red}{-9+2}\color{blue}{-2i -10i}=\color{red}{-7}\color{blue}{-12i}\)
6. \((-3-4i)\cdot (+4i)= -12 i-16i^2 = \color{red}{16}\color{blue}{-12i}\)
7. \((-7+8i)-(-4-10i)= -7+8i +4+10i =\color{red}{-7+4}\color{blue}{+8i +10i}=\color{red}{-3}\color{blue}{+18i}\)
8. \((-1+6i) \cdot (6+8i)= -6-8i +36 i+48i^2 = -6-8i +36 i-48= \color{red}{-6-48}\color{blue}{-8i +36i}=\color{red}{-54}\color{blue}{+28i}\)
9. \((7+3i)-(-10-6i)= 7+3i +10+6i =\color{red}{7+10}\color{blue}{+3i +6i}=\color{red}{17}\color{blue}{+9i}\)
10. \(\frac{9-3i}{2+2i}= \frac{9-3i}{2+2i} \cdot \frac{2-2i}{2-2i} = \frac{18-18i -6 i+6i^2 }{(2)^2-(2i)^2} = \frac{18-18i -6 i-6}{4 + 4} = \frac{12-24i }{8} = \frac{3}{2} + 3i\)
11. \((3+5i) \cdot (-1-4i)= -3-12i -5 i-20i^2 = -3-12i -5 i+20= \color{red}{-3+20}\color{blue}{-12i -5i}=\color{red}{17}\color{blue}{-17i}\)
12. \((-8-6i) \cdot (5+3i)= -40-24i -30 i-18i^2 = -40-24i -30 i+18= \color{red}{-40+18}\color{blue}{-24i -30i}=\color{red}{-22}\color{blue}{-54i}\)