Basisbewerkingen gemengd (a+bi)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \((5+6i)-(-9+5i)= 5+6i +9-5i =\color{red}{5+9}\color{blue}{+6i -5i}=\color{red}{14}\color{blue}{+i}\)
2. \((-7-7i) \cdot (-10+i)= 70-7i +70 i-7i^2 = 70-7i +70 i+7= \color{red}{70+7}\color{blue}{-7i +70i}=\color{red}{77}\color{blue}{+63i}\)
3. \((5+i)+(6+i)= 5+i +6+i =\color{red}{5+6}\color{blue}{+i +i}=\color{red}{11}\color{blue}{+2i}\)
4. \((-3-2i)\cdot (+6i)= -18 i-12i^2 = \color{red}{12}\color{blue}{-18i}\)
5. \(\frac{-3+4i}{6+4i}= \frac{-3+4i}{6+4i} \cdot \frac{6-4i}{6-4i} = \frac{-18+12i +24 i-16i^2 }{(6)^2-(4i)^2} = \frac{-18+12i +24 i+16}{36 + 16} = \frac{-2+36i }{52} = \frac{-1}{26} - \frac{-9}{13}i \)
6. \((1-i)-(-1-5i)= 1-i +1+5i =\color{red}{1+1}\color{blue}{-i +5i}=\color{red}{2}\color{blue}{+4i}\)
7. \(\frac{-6+10i}{8-9i}= \frac{-6+10i}{8-9i} \cdot \frac{8+9i}{8+9i} = \frac{-48-54i +80 i+90i^2 }{(8)^2-(-9i)^2} = \frac{-48-54i +80 i-90}{64 + 81} = \frac{-138+26i }{145} = \frac{-138}{145} - \frac{-26}{145}i \)
8. \((+3i) \cdot (10-4i)= +30 i-12i^2 = \color{red}{12}\color{blue}{+30i}\)
9. \((-8-i)\cdot (-3i)= +24 i+3i^2 = \color{red}{-3}\color{blue}{+24i}\)
10. \((8+5i)+(3+5i)= 8+5i +3+5i =\color{red}{8+3}\color{blue}{+5i +5i}=\color{red}{11}\color{blue}{+10i}\)
11. \((10-6i)\cdot (+9i)= +90 i-54i^2 = \color{red}{54}\color{blue}{+90i}\)
12. \((-7+7i)+(-4+5i)= -7+7i -4+5i =\color{red}{-7-4}\color{blue}{+7i +5i}=\color{red}{-11}\color{blue}{+12i}\)