Vermenigvuldigen en delen (a+bi)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \((-2-6i) \cdot (6-7i)= -12+14i -36 i+42i^2 = -12+14i -36 i-42= \color{red}{-12-42}\color{blue}{+14i -36i}=\color{red}{-54}\color{blue}{-22i}\)
2. \(\frac{8-6i}{8+10i}= \frac{8-6i}{8+10i} \cdot \frac{8-10i}{8-10i} = \frac{64-80i -48 i+60i^2 }{(8)^2-(10i)^2} = \frac{64-80i -48 i-60}{64 + 100} = \frac{4-128i }{164} = \frac{1}{41} + \frac{-32}{41}i \)
3. \((-10i) \cdot (-4+10i)= +40 i-100i^2 = \color{red}{100}\color{blue}{+40i}\)
4. \((-9+9i) \cdot (6+3i)= -54-27i +54 i+27i^2 = -54-27i +54 i-27= \color{red}{-54-27}\color{blue}{-27i +54i}=\color{red}{-81}\color{blue}{+27i}\)
5. \((-9-4i) \cdot (-5-9i)= 45+81i +20 i+36i^2 = 45+81i +20 i-36= \color{red}{45-36}\color{blue}{+81i +20i}=\color{red}{9}\color{blue}{+101i}\)
6. \((7+5i) \cdot (-3-8i)= -21-56i -15 i-40i^2 = -21-56i -15 i+40= \color{red}{-21+40}\color{blue}{-56i -15i}=\color{red}{19}\color{blue}{-71i}\)
7. \(\frac{-10-2i}{-1-i}= \frac{-10-2i}{-1-i} \cdot \frac{-1+i}{-1+i} = \frac{10-10i +2 i-2i^2 }{(-1)^2-(-1i)^2} = \frac{10-10i +2 i+2}{1 + 1} = \frac{12-8i }{2} = 6+ 4i\)
8. \((-1+4i) \cdot (-5+10i)= 5-10i -20 i+40i^2 = 5-10i -20 i-40= \color{red}{5-40}\color{blue}{-10i -20i}=\color{red}{-35}\color{blue}{-30i}\)
9. \((8-6i)\cdot (+8i)= +64 i-48i^2 = \color{red}{48}\color{blue}{+64i}\)
10. \((-6+i) \cdot (-1+4i)= 6-24i -1 i+4i^2 = 6-24i -1 i-4= \color{red}{6-4}\color{blue}{-24i -i}=\color{red}{2}\color{blue}{-25i}\)
11. \((5-9i)\cdot (-9i)= -45 i+81i^2 = \color{red}{-81}\color{blue}{-45i}\)
12. \(\frac{4-8i}{-2-4i}= \frac{4-8i}{-2-4i} \cdot \frac{-2+4i}{-2+4i} = \frac{-8+16i +16 i-32i^2 }{(-2)^2-(-4i)^2} = \frac{-8+16i +16 i+32}{4 + 16} = \frac{24+32i }{20} = \frac{6}{5} - \frac{-8}{5}i \)