Vermenigvuldigen en delen (a+bi)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(\frac{1-9i}{6-9i}= \frac{1-9i}{6-9i} \cdot \frac{6+9i}{6+9i} = \frac{6+9i -54 i-81i^2 }{(6)^2-(-9i)^2} = \frac{6+9i -54 i+81}{36 + 81} = \frac{87-45i }{117} = \frac{29}{39} + \frac{-5}{13}i \)
2. \((-2-4i) \cdot (2-9i)= -4+18i -8 i+36i^2 = -4+18i -8 i-36= \color{red}{-4-36}\color{blue}{+18i -8i}=\color{red}{-40}\color{blue}{+10i}\)
3. \(\frac{-1-6i}{-5-7i}= \frac{-1-6i}{-5-7i} \cdot \frac{-5+7i}{-5+7i} = \frac{5-7i +30 i-42i^2 }{(-5)^2-(-7i)^2} = \frac{5-7i +30 i+42}{25 + 49} = \frac{47+23i }{74} = \frac{47}{74} - \frac{-23}{74}i \)
4. \((-2+3i) \cdot (10-8i)= -20+16i +30 i-24i^2 = -20+16i +30 i+24= \color{red}{-20+24}\color{blue}{+16i +30i}=\color{red}{4}\color{blue}{+46i}\)
5. \(\frac{-6-6i}{8+i}= \frac{-6-6i}{8+i} \cdot \frac{8-i}{8-i} = \frac{-48+6i -48 i+6i^2 }{(8)^2-(1i)^2} = \frac{-48+6i -48 i-6}{64 + 1} = \frac{-54-42i }{65} = \frac{-54}{65} + \frac{-42}{65}i \)
6. \((+8i) \cdot (-5+9i)= -40 i+72i^2 = \color{red}{-72}\color{blue}{-40i}\)
7. \((+10i) \cdot (5-7i)= +50 i-70i^2 = \color{red}{70}\color{blue}{+50i}\)
8. \((9+5i) \cdot (8-4i)= 72-36i +40 i-20i^2 = 72-36i +40 i+20= \color{red}{72+20}\color{blue}{-36i +40i}=\color{red}{92}\color{blue}{+4i}\)
9. \((-10+8i)\cdot (+2i)= -20 i+16i^2 = \color{red}{-16}\color{blue}{-20i}\)
10. \(\frac{-5+5i}{-3-2i}= \frac{-5+5i}{-3-2i} \cdot \frac{-3+2i}{-3+2i} = \frac{15-10i -15 i+10i^2 }{(-3)^2-(-2i)^2} = \frac{15-10i -15 i-10}{9 + 4} = \frac{5-25i }{13} = \frac{5}{13} + \frac{-25}{13}i \)
11. \((-2-10i) \cdot (-4-2i)= 8+4i +40 i+20i^2 = 8+4i +40 i-20= \color{red}{8-20}\color{blue}{+4i +40i}=\color{red}{-12}\color{blue}{+44i}\)
12. \((1-i)\cdot (-9i)= -9 i+9i^2 = \color{red}{-9}\color{blue}{-9i}\)