Vermenigvuldigen en delen (a+bi)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \((-7+4i) \cdot (9-7i)= -63+49i +36 i-28i^2 = -63+49i +36 i+28= \color{red}{-63+28}\color{blue}{+49i +36i}=\color{red}{-35}\color{blue}{+85i}\)
2. \((1-7i)\cdot (-i)= -1 i+7i^2 = \color{red}{-7}\color{blue}{-i}\)
3. \((+8i) \cdot (8-8i)= +64 i-64i^2 = \color{red}{64}\color{blue}{+64i}\)
4. \((7-10i) \cdot (-8-5i)= -56-35i +80 i+50i^2 = -56-35i +80 i-50= \color{red}{-56-50}\color{blue}{-35i +80i}=\color{red}{-106}\color{blue}{+45i}\)
5. \((-8-2i) \cdot (6-10i)= -48+80i -12 i+20i^2 = -48+80i -12 i-20= \color{red}{-48-20}\color{blue}{+80i -12i}=\color{red}{-68}\color{blue}{+68i}\)
6. \((+7i) \cdot (-9+3i)= -63 i+21i^2 = \color{red}{-21}\color{blue}{-63i}\)
7. \((+10i) \cdot (6-7i)= +60 i-70i^2 = \color{red}{70}\color{blue}{+60i}\)
8. \(\frac{2+2i}{-7-2i}= \frac{2+2i}{-7-2i} \cdot \frac{-7+2i}{-7+2i} = \frac{-14+4i -14 i+4i^2 }{(-7)^2-(-2i)^2} = \frac{-14+4i -14 i-4}{49 + 4} = \frac{-18-10i }{53} = \frac{-18}{53} + \frac{-10}{53}i \)
9. \((10+i)\cdot (-3i)= -30 i-3i^2 = \color{red}{3}\color{blue}{-30i}\)
10. \((-5i) \cdot (-8+6i)= +40 i-30i^2 = \color{red}{30}\color{blue}{+40i}\)
11. \(\frac{7+8i}{-4+8i}= \frac{7+8i}{-4+8i} \cdot \frac{-4-8i}{-4-8i} = \frac{-28-56i -32 i-64i^2 }{(-4)^2-(8i)^2} = \frac{-28-56i -32 i+64}{16 + 64} = \frac{36-88i }{80} = \frac{9}{20} + \frac{-11}{10}i \)
12. \((9-i)\cdot (+i)= +9 i-i^2 = \color{red}{1}\color{blue}{+9i}\)