Basisbewerkingen gemengd (a+bi)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \((-2+2i)\cdot (+i)= -2 i+2i^2 = \color{red}{-2}\color{blue}{-2i}\)
2. \((-7-i)+(6-2i)= -7-i +6-2i =\color{red}{-7+6}\color{blue}{-i -2i}=\color{red}{-1}\color{blue}{-3i}\)
3. \((7+i)\cdot (-8i)= -56 i-8i^2 = \color{red}{8}\color{blue}{-56i}\)
4. \((-6i) \cdot (6+5i)= -36 i-30i^2 = \color{red}{30}\color{blue}{-36i}\)
5. \((4+7i) \cdot (-5+3i)= -20+12i -35 i+21i^2 = -20+12i -35 i-21= \color{red}{-20-21}\color{blue}{+12i -35i}=\color{red}{-41}\color{blue}{-23i}\)
6. \((-5+2i)+(-7+3i)= -5+2i -7+3i =\color{red}{-5-7}\color{blue}{+2i +3i}=\color{red}{-12}\color{blue}{+5i}\)
7. \(\frac{3+i}{-1+6i}= \frac{3+i}{-1+6i} \cdot \frac{-1-6i}{-1-6i} = \frac{-3-18i -1 i-6i^2 }{(-1)^2-(6i)^2} = \frac{-3-18i -1 i+6}{1 + 36} = \frac{3-19i }{37} = \frac{3}{37} + \frac{-19}{37}i \)
8. \((-7+8i)+(6+9i)= -7+8i +6+9i =\color{red}{-7+6}\color{blue}{+8i +9i}=\color{red}{-1}\color{blue}{+17i}\)
9. \(\frac{10-i}{7+3i}= \frac{10-i}{7+3i} \cdot \frac{7-3i}{7-3i} = \frac{70-30i -7 i+3i^2 }{(7)^2-(3i)^2} = \frac{70-30i -7 i-3}{49 + 9} = \frac{67-37i }{58} = \frac{67}{58} + \frac{-37}{58}i \)
10. \((-5+2i) \cdot (-8+5i)= 40-25i -16 i+10i^2 = 40-25i -16 i-10= \color{red}{40-10}\color{blue}{-25i -16i}=\color{red}{30}\color{blue}{-41i}\)
11. \(\frac{3+2i}{8+8i}= \frac{3+2i}{8+8i} \cdot \frac{8-8i}{8-8i} = \frac{24-24i +16 i-16i^2 }{(8)^2-(8i)^2} = \frac{24-24i +16 i+16}{64 + 64} = \frac{40-8i }{128} = \frac{5}{16} + \frac{-1}{16}i \)
12. \((-6-2i)+(10-7i)= -6-2i +10-7i =\color{red}{-6+10}\color{blue}{-2i -7i}=\color{red}{4}\color{blue}{-9i}\)