Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((10-5i) \cdot (7+4i)= 70+40i -35 i-20i^2 = 70+40i -35 i+20= \color{red}{70+20}\color{blue}{+40i -35i}=\color{red}{90}\color{blue}{+5i}\)
2. \((-5-3i)\cdot (-5i)= +25 i+15i^2 = \color{red}{-15}\color{blue}{+25i}\)
3. \((-3+9i) \cdot (4+i)= -12-3i +36 i+9i^2 = -12-3i +36 i-9= \color{red}{-12-9}\color{blue}{-3i +36i}=\color{red}{-21}\color{blue}{+33i}\)
4. \((7+6i) \cdot (6-10i)= 42-70i +36 i-60i^2 = 42-70i +36 i+60= \color{red}{42+60}\color{blue}{-70i +36i}=\color{red}{102}\color{blue}{-34i}\)
5. \((+3i) \cdot (9-8i)= +27 i-24i^2 = \color{red}{24}\color{blue}{+27i}\)
6. \((1-6i) \cdot (-10+5i)= -10+5i +60 i-30i^2 = -10+5i +60 i+30= \color{red}{-10+30}\color{blue}{+5i +60i}=\color{red}{20}\color{blue}{+65i}\)
7. \((10+2i) \cdot (5+i)= 50+10i +10 i+2i^2 = 50+10i +10 i-2= \color{red}{50-2}\color{blue}{+10i +10i}=\color{red}{48}\color{blue}{+20i}\)
8. \((-7+i)\cdot (-7i)= +49 i-7i^2 = \color{red}{7}\color{blue}{+49i}\)
9. \(\frac{-2+5i}{-10+8i}= \frac{-2+5i}{-10+8i} \cdot \frac{-10-8i}{-10-8i} = \frac{20+16i -50 i-40i^2 }{(-10)^2-(8i)^2} = \frac{20+16i -50 i+40}{100 + 64} = \frac{60-34i }{164} = \frac{15}{41} + \frac{-17}{82}i \)
10. \(\frac{-7+8i}{6-3i}= \frac{-7+8i}{6-3i} \cdot \frac{6+3i}{6+3i} = \frac{-42-21i +48 i+24i^2 }{(6)^2-(-3i)^2} = \frac{-42-21i +48 i-24}{36 + 9} = \frac{-66+27i }{45} = \frac{-22}{15} - \frac{-3}{5}i \)
11. \(\frac{3-6i}{6+6i}= \frac{3-6i}{6+6i} \cdot \frac{6-6i}{6-6i} = \frac{18-18i -36 i+36i^2 }{(6)^2-(6i)^2} = \frac{18-18i -36 i-36}{36 + 36} = \frac{-18-54i }{72} = \frac{-1}{4} + \frac{-3}{4}i \)
12. \((6+2i) \cdot (-5-2i)= -30-12i -10 i-4i^2 = -30-12i -10 i+4= \color{red}{-30+4}\color{blue}{-12i -10i}=\color{red}{-26}\color{blue}{-22i}\)