Basisbewerkingen gemengd (a+bi)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \((-10+10i)-(-1+9i)= -10+10i +1-9i =\color{red}{-10+1}\color{blue}{+10i -9i}=\color{red}{-9}\color{blue}{+i}\)
2. \((6+4i) \cdot (7+8i)= 42+48i +28 i+32i^2 = 42+48i +28 i-32= \color{red}{42-32}\color{blue}{+48i +28i}=\color{red}{10}\color{blue}{+76i}\)
3. \((-5-2i)\cdot (-7i)= +35 i+14i^2 = \color{red}{-14}\color{blue}{+35i}\)
4. \((-8i) \cdot (1-2i)= -8 i+16i^2 = \color{red}{-16}\color{blue}{-8i}\)
5. \((5-2i)+(7+3i)= 5-2i +7+3i =\color{red}{5+7}\color{blue}{-2i +3i}=\color{red}{12}\color{blue}{+i}\)
6. \((2+6i)-(10+4i)= 2+6i -10-4i =\color{red}{2-10}\color{blue}{+6i -4i}=\color{red}{-8}\color{blue}{+2i}\)
7. \((+3i) \cdot (-8+3i)= -24 i+9i^2 = \color{red}{-9}\color{blue}{-24i}\)
8. \((5+i)+(-2+5i)= 5+i -2+5i =\color{red}{5-2}\color{blue}{+i +5i}=\color{red}{3}\color{blue}{+6i}\)
9. \(\frac{7-8i}{-1+10i}= \frac{7-8i}{-1+10i} \cdot \frac{-1-10i}{-1-10i} = \frac{-7-70i +8 i+80i^2 }{(-1)^2-(10i)^2} = \frac{-7-70i +8 i-80}{1 + 100} = \frac{-87-62i }{101} = \frac{-87}{101} + \frac{-62}{101}i \)
10. \(\frac{-8-9i}{-5+9i}= \frac{-8-9i}{-5+9i} \cdot \frac{-5-9i}{-5-9i} = \frac{40+72i +45 i+81i^2 }{(-5)^2-(9i)^2} = \frac{40+72i +45 i-81}{25 + 81} = \frac{-41+117i }{106} = \frac{-41}{106} - \frac{-117}{106}i \)
11. \((-10+7i)+(4+3i)= -10+7i +4+3i =\color{red}{-10+4}\color{blue}{+7i +3i}=\color{red}{-6}\color{blue}{+10i}\)
12. \((3-i)+(-6-i)= 3-i -6-i =\color{red}{3-6}\color{blue}{-i -i}=\color{red}{-3}\color{blue}{-2i}\)