Basisbewerkingen gemengd (a+bi)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \((+5i) \cdot (1+4i)= +5 i+20i^2 = \color{red}{-20}\color{blue}{+5i}\)
2. \((+3i) \cdot (9+8i)= +27 i+24i^2 = \color{red}{-24}\color{blue}{+27i}\)
3. \((-6+9i) \cdot (-1-3i)= 6+18i -9 i-27i^2 = 6+18i -9 i+27= \color{red}{6+27}\color{blue}{+18i -9i}=\color{red}{33}\color{blue}{+9i}\)
4. \((-i) \cdot (1+7i)= -1 i-7i^2 = \color{red}{7}\color{blue}{-i}\)
5. \((-3-9i)+(2+9i)= -3-9i +2+9i =\color{red}{-3+2}\color{blue}{-9i +9i}=\color{red}{-1}\)
6. \(\frac{-2-7i}{1+10i}= \frac{-2-7i}{1+10i} \cdot \frac{1-10i}{1-10i} = \frac{-2+20i -7 i+70i^2 }{(1)^2-(10i)^2} = \frac{-2+20i -7 i-70}{1 + 100} = \frac{-72+13i }{101} = \frac{-72}{101} - \frac{-13}{101}i \)
7. \((-2+i) \cdot (7-5i)= -14+10i +7 i-5i^2 = -14+10i +7 i+5= \color{red}{-14+5}\color{blue}{+10i +7i}=\color{red}{-9}\color{blue}{+17i}\)
8. \((-2+2i)-(3-3i)= -2+2i -3+3i =\color{red}{-2-3}\color{blue}{+2i +3i}=\color{red}{-5}\color{blue}{+5i}\)
9. \(\frac{-3+2i}{-8-i}= \frac{-3+2i}{-8-i} \cdot \frac{-8+i}{-8+i} = \frac{24-3i -16 i+2i^2 }{(-8)^2-(-1i)^2} = \frac{24-3i -16 i-2}{64 + 1} = \frac{22-19i }{65} = \frac{22}{65} + \frac{-19}{65}i \)
10. \((7+8i)-(1+6i)= 7+8i -1-6i =\color{red}{7-1}\color{blue}{+8i -6i}=\color{red}{6}\color{blue}{+2i}\)
11. \(\frac{4-10i}{-1-4i}= \frac{4-10i}{-1-4i} \cdot \frac{-1+4i}{-1+4i} = \frac{-4+16i +10 i-40i^2 }{(-1)^2-(-4i)^2} = \frac{-4+16i +10 i+40}{1 + 16} = \frac{36+26i }{17} = \frac{36}{17} - \frac{-26}{17}i \)
12. \((-6-3i)+(-4-5i)= -6-3i -4-5i =\color{red}{-6-4}\color{blue}{-3i -5i}=\color{red}{-10}\color{blue}{-8i}\)