Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-5i) \cdot (-8+5i)= +40 i-25i^2 = \color{red}{25}\color{blue}{+40i}\)
2. \(\frac{9+2i}{-3-10i}= \frac{9+2i}{-3-10i} \cdot \frac{-3+10i}{-3+10i} = \frac{-27+90i -6 i+20i^2 }{(-3)^2-(-10i)^2} = \frac{-27+90i -6 i-20}{9 + 100} = \frac{-47+84i }{109} = \frac{-47}{109} - \frac{-84}{109}i \)
3. \(\frac{3-9i}{-3+4i}= \frac{3-9i}{-3+4i} \cdot \frac{-3-4i}{-3-4i} = \frac{-9-12i +27 i+36i^2 }{(-3)^2-(4i)^2} = \frac{-9-12i +27 i-36}{9 + 16} = \frac{-45+15i }{25} = \frac{-9}{5} - \frac{-3}{5}i \)
4. \((-6-2i) \cdot (1-5i)= -6+30i -2 i+10i^2 = -6+30i -2 i-10= \color{red}{-6-10}\color{blue}{+30i -2i}=\color{red}{-16}\color{blue}{+28i}\)
5. \((+6i) \cdot (10-6i)= +60 i-36i^2 = \color{red}{36}\color{blue}{+60i}\)
6. \((-2i) \cdot (10+i)= -20 i-2i^2 = \color{red}{2}\color{blue}{-20i}\)
7. \(\frac{-9-9i}{-2+7i}= \frac{-9-9i}{-2+7i} \cdot \frac{-2-7i}{-2-7i} = \frac{18+63i +18 i+63i^2 }{(-2)^2-(7i)^2} = \frac{18+63i +18 i-63}{4 + 49} = \frac{-45+81i }{53} = \frac{-45}{53} - \frac{-81}{53}i \)
8. \((8-9i) \cdot (-7-5i)= -56-40i +63 i+45i^2 = -56-40i +63 i-45= \color{red}{-56-45}\color{blue}{-40i +63i}=\color{red}{-101}\color{blue}{+23i}\)
9. \((-5+7i) \cdot (-4-7i)= 20+35i -28 i-49i^2 = 20+35i -28 i+49= \color{red}{20+49}\color{blue}{+35i -28i}=\color{red}{69}\color{blue}{+7i}\)
10. \((-8i) \cdot (8+3i)= -64 i-24i^2 = \color{red}{24}\color{blue}{-64i}\)
11. \((10+5i) \cdot (-1+5i)= -10+50i -5 i+25i^2 = -10+50i -5 i-25= \color{red}{-10-25}\color{blue}{+50i -5i}=\color{red}{-35}\color{blue}{+45i}\)
12. \((-10-8i) \cdot (10+10i)= -100-100i -80 i-80i^2 = -100-100i -80 i+80= \color{red}{-100+80}\color{blue}{-100i -80i}=\color{red}{-20}\color{blue}{-180i}\)