Basisbewerkingen gemengd (a+bi)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \((9-9i) \cdot (1-4i)= 9-36i -9 i+36i^2 = 9-36i -9 i-36= \color{red}{9-36}\color{blue}{-36i -9i}=\color{red}{-27}\color{blue}{-45i}\)
2. \(\frac{-2-8i}{-8-9i}= \frac{-2-8i}{-8-9i} \cdot \frac{-8+9i}{-8+9i} = \frac{16-18i +64 i-72i^2 }{(-8)^2-(-9i)^2} = \frac{16-18i +64 i+72}{64 + 81} = \frac{88+46i }{145} = \frac{88}{145} - \frac{-46}{145}i \)
3. \((-2+7i) \cdot (-8+9i)= 16-18i -56 i+63i^2 = 16-18i -56 i-63= \color{red}{16-63}\color{blue}{-18i -56i}=\color{red}{-47}\color{blue}{-74i}\)
4. \((8+8i) \cdot (4+2i)= 32+16i +32 i+16i^2 = 32+16i +32 i-16= \color{red}{32-16}\color{blue}{+16i +32i}=\color{red}{16}\color{blue}{+48i}\)
5. \((+i) \cdot (-5-4i)= -5 i-4i^2 = \color{red}{4}\color{blue}{-5i}\)
6. \((-4-3i) \cdot (10+3i)= -40-12i -30 i-9i^2 = -40-12i -30 i+9= \color{red}{-40+9}\color{blue}{-12i -30i}=\color{red}{-31}\color{blue}{-42i}\)
7. \((-7+3i)\cdot (-5i)= +35 i-15i^2 = \color{red}{15}\color{blue}{+35i}\)
8. \(\frac{-1+i}{-8-3i}= \frac{-1+i}{-8-3i} \cdot \frac{-8+3i}{-8+3i} = \frac{8-3i -8 i+3i^2 }{(-8)^2-(-3i)^2} = \frac{8-3i -8 i-3}{64 + 9} = \frac{5-11i }{73} = \frac{5}{73} + \frac{-11}{73}i \)
9. \((-5-10i) \cdot (2-i)= -10+5i -20 i+10i^2 = -10+5i -20 i-10= \color{red}{-10-10}\color{blue}{+5i -20i}=\color{red}{-20}\color{blue}{-15i}\)
10. \((-8+3i)-(3-6i)= -8+3i -3+6i =\color{red}{-8-3}\color{blue}{+3i +6i}=\color{red}{-11}\color{blue}{+9i}\)
11. \((-4-6i) \cdot (9+6i)= -36-24i -54 i-36i^2 = -36-24i -54 i+36= \color{red}{-36+36}\color{blue}{-24i -54i}=\color{blue}{-78i}\)
12. \(\frac{-3-2i}{5+2i}= \frac{-3-2i}{5+2i} \cdot \frac{5-2i}{5-2i} = \frac{-15+6i -10 i+4i^2 }{(5)^2-(2i)^2} = \frac{-15+6i -10 i-4}{25 + 4} = \frac{-19-4i }{29} = \frac{-19}{29} + \frac{-4}{29}i \)