Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-5+3i) \cdot (-8-3i)= 40+15i -24 i-9i^2 = 40+15i -24 i+9= \color{red}{40+9}\color{blue}{+15i -24i}=\color{red}{49}\color{blue}{-9i}\)
2. \((-2+9i) \cdot (1-8i)= -2+16i +9 i-72i^2 = -2+16i +9 i+72= \color{red}{-2+72}\color{blue}{+16i +9i}=\color{red}{70}\color{blue}{+25i}\)
3. \((8-4i) \cdot (-10-6i)= -80-48i +40 i+24i^2 = -80-48i +40 i-24= \color{red}{-80-24}\color{blue}{-48i +40i}=\color{red}{-104}\color{blue}{-8i}\)
4. \(\frac{-5+5i}{4-3i}= \frac{-5+5i}{4-3i} \cdot \frac{4+3i}{4+3i} = \frac{-20-15i +20 i+15i^2 }{(4)^2-(-3i)^2} = \frac{-20-15i +20 i-15}{16 + 9} = \frac{-35+5i }{25} = \frac{-7}{5} - \frac{-1}{5}i \)
5. \((5+10i)\cdot (+i)= +5 i+10i^2 = \color{red}{-10}\color{blue}{+5i}\)
6. \(\frac{-6+2i}{-2-2i}= \frac{-6+2i}{-2-2i} \cdot \frac{-2+2i}{-2+2i} = \frac{12-12i -4 i+4i^2 }{(-2)^2-(-2i)^2} = \frac{12-12i -4 i-4}{4 + 4} = \frac{8-16i }{8} = 1+ 2i\)
7. \((10+4i)\cdot (-8i)= -80 i-32i^2 = \color{red}{32}\color{blue}{-80i}\)
8. \((3-6i)\cdot (+i)= +3 i-6i^2 = \color{red}{6}\color{blue}{+3i}\)
9. \(\frac{2-10i}{-10-4i}= \frac{2-10i}{-10-4i} \cdot \frac{-10+4i}{-10+4i} = \frac{-20+8i +100 i-40i^2 }{(-10)^2-(-4i)^2} = \frac{-20+8i +100 i+40}{100 + 16} = \frac{20+108i }{116} = \frac{5}{29} - \frac{-27}{29}i \)
10. \((2+3i) \cdot (-2+6i)= -4+12i -6 i+18i^2 = -4+12i -6 i-18= \color{red}{-4-18}\color{blue}{+12i -6i}=\color{red}{-22}\color{blue}{+6i}\)
11. \((6+10i) \cdot (6-9i)= 36-54i +60 i-90i^2 = 36-54i +60 i+90= \color{red}{36+90}\color{blue}{-54i +60i}=\color{red}{126}\color{blue}{+6i}\)
12. \(\frac{-5+4i}{-10+6i}= \frac{-5+4i}{-10+6i} \cdot \frac{-10-6i}{-10-6i} = \frac{50+30i -40 i-24i^2 }{(-10)^2-(6i)^2} = \frac{50+30i -40 i+24}{100 + 36} = \frac{74-10i }{136} = \frac{37}{68} + \frac{-5}{68}i \)