Vermenigvuldigen en delen (a+bi)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(\frac{-6-6i}{4-9i}= \frac{-6-6i}{4-9i} \cdot \frac{4+9i}{4+9i} = \frac{-24-54i -24 i-54i^2 }{(4)^2-(-9i)^2} = \frac{-24-54i -24 i+54}{16 + 81} = \frac{30-78i }{97} = \frac{30}{97} + \frac{-78}{97}i \)
2. \((-10+2i)\cdot (-8i)= +80 i-16i^2 = \color{red}{16}\color{blue}{+80i}\)
3. \(\frac{-9+2i}{-2+9i}= \frac{-9+2i}{-2+9i} \cdot \frac{-2-9i}{-2-9i} = \frac{18+81i -4 i-18i^2 }{(-2)^2-(9i)^2} = \frac{18+81i -4 i+18}{4 + 81} = \frac{36+77i }{85} = \frac{36}{85} - \frac{-77}{85}i \)
4. \((-7-i)\cdot (+2i)= -14 i-2i^2 = \color{red}{2}\color{blue}{-14i}\)
5. \((2-8i) \cdot (-3+5i)= -6+10i +24 i-40i^2 = -6+10i +24 i+40= \color{red}{-6+40}\color{blue}{+10i +24i}=\color{red}{34}\color{blue}{+34i}\)
6. \((-2-3i)\cdot (+7i)= -14 i-21i^2 = \color{red}{21}\color{blue}{-14i}\)
7. \(\frac{-7-10i}{-8-5i}= \frac{-7-10i}{-8-5i} \cdot \frac{-8+5i}{-8+5i} = \frac{56-35i +80 i-50i^2 }{(-8)^2-(-5i)^2} = \frac{56-35i +80 i+50}{64 + 25} = \frac{106+45i }{89} = \frac{106}{89} - \frac{-45}{89}i \)
8. \((6+3i) \cdot (10+2i)= 60+12i +30 i+6i^2 = 60+12i +30 i-6= \color{red}{60-6}\color{blue}{+12i +30i}=\color{red}{54}\color{blue}{+42i}\)
9. \(\frac{10+9i}{-2-4i}= \frac{10+9i}{-2-4i} \cdot \frac{-2+4i}{-2+4i} = \frac{-20+40i -18 i+36i^2 }{(-2)^2-(-4i)^2} = \frac{-20+40i -18 i-36}{4 + 16} = \frac{-56+22i }{20} = \frac{-14}{5} - \frac{-11}{10}i \)
10. \((-8+5i)\cdot (+8i)= -64 i+40i^2 = \color{red}{-40}\color{blue}{-64i}\)
11. \((-8+i) \cdot (-2-8i)= 16+64i -2 i-8i^2 = 16+64i -2 i+8= \color{red}{16+8}\color{blue}{+64i -2i}=\color{red}{24}\color{blue}{+62i}\)
12. \((7-5i) \cdot (-7+3i)= -49+21i +35 i-15i^2 = -49+21i +35 i+15= \color{red}{-49+15}\color{blue}{+21i +35i}=\color{red}{-34}\color{blue}{+56i}\)