Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \(\frac{7-3i}{10+4i}= \frac{7-3i}{10+4i} \cdot \frac{10-4i}{10-4i} = \frac{70-28i -30 i+12i^2 }{(10)^2-(4i)^2} = \frac{70-28i -30 i-12}{100 + 16} = \frac{58-58i }{116} = \frac{1}{2} + \frac{-1}{2}i \)
2. \((-7+8i)\cdot (+6i)= -42 i+48i^2 = \color{red}{-48}\color{blue}{-42i}\)
3. \((+3i) \cdot (10+10i)= +30 i+30i^2 = \color{red}{-30}\color{blue}{+30i}\)
4. \(\frac{5-4i}{-8-5i}= \frac{5-4i}{-8-5i} \cdot \frac{-8+5i}{-8+5i} = \frac{-40+25i +32 i-20i^2 }{(-8)^2-(-5i)^2} = \frac{-40+25i +32 i+20}{64 + 25} = \frac{-20+57i }{89} = \frac{-20}{89} - \frac{-57}{89}i \)
5. \(\frac{10+6i}{-5+6i}= \frac{10+6i}{-5+6i} \cdot \frac{-5-6i}{-5-6i} = \frac{-50-60i -30 i-36i^2 }{(-5)^2-(6i)^2} = \frac{-50-60i -30 i+36}{25 + 36} = \frac{-14-90i }{61} = \frac{-14}{61} + \frac{-90}{61}i \)
6. \(\frac{5+9i}{-2+4i}= \frac{5+9i}{-2+4i} \cdot \frac{-2-4i}{-2-4i} = \frac{-10-20i -18 i-36i^2 }{(-2)^2-(4i)^2} = \frac{-10-20i -18 i+36}{4 + 16} = \frac{26-38i }{20} = \frac{13}{10} + \frac{-19}{10}i \)
7. \((-9+6i) \cdot (5+8i)= -45-72i +30 i+48i^2 = -45-72i +30 i-48= \color{red}{-45-48}\color{blue}{-72i +30i}=\color{red}{-93}\color{blue}{-42i}\)
8. \((-10-i) \cdot (6+5i)= -60-50i -6 i-5i^2 = -60-50i -6 i+5= \color{red}{-60+5}\color{blue}{-50i -6i}=\color{red}{-55}\color{blue}{-56i}\)
9. \(\frac{-8-3i}{-1-3i}= \frac{-8-3i}{-1-3i} \cdot \frac{-1+3i}{-1+3i} = \frac{8-24i +3 i-9i^2 }{(-1)^2-(-3i)^2} = \frac{8-24i +3 i+9}{1 + 9} = \frac{17-21i }{10} = \frac{17}{10} + \frac{-21}{10}i \)
10. \(\frac{-5-9i}{5+4i}= \frac{-5-9i}{5+4i} \cdot \frac{5-4i}{5-4i} = \frac{-25+20i -45 i+36i^2 }{(5)^2-(4i)^2} = \frac{-25+20i -45 i-36}{25 + 16} = \frac{-61-25i }{41} = \frac{-61}{41} + \frac{-25}{41}i \)
11. \((-4-2i) \cdot (-5+3i)= 20-12i +10 i-6i^2 = 20-12i +10 i+6= \color{red}{20+6}\color{blue}{-12i +10i}=\color{red}{26}\color{blue}{-2i}\)
12. \(\frac{-9-7i}{8-2i}= \frac{-9-7i}{8-2i} \cdot \frac{8+2i}{8+2i} = \frac{-72-18i -56 i-14i^2 }{(8)^2-(-2i)^2} = \frac{-72-18i -56 i+14}{64 + 4} = \frac{-58-74i }{68} = \frac{-29}{34} + \frac{-37}{34}i \)