Vermenigvuldigen en delen (a+bi)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(\frac{-8-2i}{-3-8i}= \frac{-8-2i}{-3-8i} \cdot \frac{-3+8i}{-3+8i} = \frac{24-64i +6 i-16i^2 }{(-3)^2-(-8i)^2} = \frac{24-64i +6 i+16}{9 + 64} = \frac{40-58i }{73} = \frac{40}{73} + \frac{-58}{73}i \)
2. \((2+10i) \cdot (-3+7i)= -6+14i -30 i+70i^2 = -6+14i -30 i-70= \color{red}{-6-70}\color{blue}{+14i -30i}=\color{red}{-76}\color{blue}{-16i}\)
3. \((-8-5i)\cdot (-9i)= +72 i+45i^2 = \color{red}{-45}\color{blue}{+72i}\)
4. \(\frac{2-2i}{8+4i}= \frac{2-2i}{8+4i} \cdot \frac{8-4i}{8-4i} = \frac{16-8i -16 i+8i^2 }{(8)^2-(4i)^2} = \frac{16-8i -16 i-8}{64 + 16} = \frac{8-24i }{80} = \frac{1}{10} + \frac{-3}{10}i \)
5. \(\frac{-8+i}{5+7i}= \frac{-8+i}{5+7i} \cdot \frac{5-7i}{5-7i} = \frac{-40+56i +5 i-7i^2 }{(5)^2-(7i)^2} = \frac{-40+56i +5 i+7}{25 + 49} = \frac{-33+61i }{74} = \frac{-33}{74} - \frac{-61}{74}i \)
6. \((8+4i) \cdot (5-10i)= 40-80i +20 i-40i^2 = 40-80i +20 i+40= \color{red}{40+40}\color{blue}{-80i +20i}=\color{red}{80}\color{blue}{-60i}\)
7. \(\frac{-9-10i}{-7-7i}= \frac{-9-10i}{-7-7i} \cdot \frac{-7+7i}{-7+7i} = \frac{63-63i +70 i-70i^2 }{(-7)^2-(-7i)^2} = \frac{63-63i +70 i+70}{49 + 49} = \frac{133+7i }{98} = \frac{19}{14} - \frac{-1}{14}i \)
8. \(\frac{-4-9i}{-2+6i}= \frac{-4-9i}{-2+6i} \cdot \frac{-2-6i}{-2-6i} = \frac{8+24i +18 i+54i^2 }{(-2)^2-(6i)^2} = \frac{8+24i +18 i-54}{4 + 36} = \frac{-46+42i }{40} = \frac{-23}{20} - \frac{-21}{20}i \)
9. \(\frac{4+4i}{-10-2i}= \frac{4+4i}{-10-2i} \cdot \frac{-10+2i}{-10+2i} = \frac{-40+8i -40 i+8i^2 }{(-10)^2-(-2i)^2} = \frac{-40+8i -40 i-8}{100 + 4} = \frac{-48-32i }{104} = \frac{-6}{13} + \frac{-4}{13}i \)
10. \((-5i) \cdot (6-5i)= -30 i+25i^2 = \color{red}{-25}\color{blue}{-30i}\)
11. \((-9i) \cdot (-10-3i)= +90 i+27i^2 = \color{red}{-27}\color{blue}{+90i}\)
12. \((-6-3i)\cdot (-8i)= +48 i+24i^2 = \color{red}{-24}\color{blue}{+48i}\)