Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \(\frac{-8+7i}{9-4i}= \frac{-8+7i}{9-4i} \cdot \frac{9+4i}{9+4i} = \frac{-72-32i +63 i+28i^2 }{(9)^2-(-4i)^2} = \frac{-72-32i +63 i-28}{81 + 16} = \frac{-100+31i }{97} = \frac{-100}{97} - \frac{-31}{97}i \)
2. \((-4i) \cdot (8+2i)= -32 i-8i^2 = \color{red}{8}\color{blue}{-32i}\)
3. \(\frac{2+8i}{5-4i}= \frac{2+8i}{5-4i} \cdot \frac{5+4i}{5+4i} = \frac{10+8i +40 i+32i^2 }{(5)^2-(-4i)^2} = \frac{10+8i +40 i-32}{25 + 16} = \frac{-22+48i }{41} = \frac{-22}{41} - \frac{-48}{41}i \)
4. \(\frac{-8-3i}{-6+3i}= \frac{-8-3i}{-6+3i} \cdot \frac{-6-3i}{-6-3i} = \frac{48+24i +18 i+9i^2 }{(-6)^2-(3i)^2} = \frac{48+24i +18 i-9}{36 + 9} = \frac{39+42i }{45} = \frac{13}{15} - \frac{-14}{15}i \)
5. \((-3-8i) \cdot (-7-6i)= 21+18i +56 i+48i^2 = 21+18i +56 i-48= \color{red}{21-48}\color{blue}{+18i +56i}=\color{red}{-27}\color{blue}{+74i}\)
6. \((-8-3i) \cdot (-5-i)= 40+8i +15 i+3i^2 = 40+8i +15 i-3= \color{red}{40-3}\color{blue}{+8i +15i}=\color{red}{37}\color{blue}{+23i}\)
7. \((3+8i) \cdot (10-5i)= 30-15i +80 i-40i^2 = 30-15i +80 i+40= \color{red}{30+40}\color{blue}{-15i +80i}=\color{red}{70}\color{blue}{+65i}\)
8. \(\frac{-10-4i}{-1+i}= \frac{-10-4i}{-1+i} \cdot \frac{-1-i}{-1-i} = \frac{10+10i +4 i+4i^2 }{(-1)^2-(1i)^2} = \frac{10+10i +4 i-4}{1 + 1} = \frac{6+14i }{2} = 3- -7i\)
9. \(\frac{-7-10i}{5+8i}= \frac{-7-10i}{5+8i} \cdot \frac{5-8i}{5-8i} = \frac{-35+56i -50 i+80i^2 }{(5)^2-(8i)^2} = \frac{-35+56i -50 i-80}{25 + 64} = \frac{-115+6i }{89} = \frac{-115}{89} - \frac{-6}{89}i \)
10. \((-1+5i) \cdot (3+10i)= -3-10i +15 i+50i^2 = -3-10i +15 i-50= \color{red}{-3-50}\color{blue}{-10i +15i}=\color{red}{-53}\color{blue}{+5i}\)
11. \(\frac{-5+5i}{-5-4i}= \frac{-5+5i}{-5-4i} \cdot \frac{-5+4i}{-5+4i} = \frac{25-20i -25 i+20i^2 }{(-5)^2-(-4i)^2} = \frac{25-20i -25 i-20}{25 + 16} = \frac{5-45i }{41} = \frac{5}{41} + \frac{-45}{41}i \)
12. \(\frac{-2-4i}{-2-2i}= \frac{-2-4i}{-2-2i} \cdot \frac{-2+2i}{-2+2i} = \frac{4-4i +8 i-8i^2 }{(-2)^2-(-2i)^2} = \frac{4-4i +8 i+8}{4 + 4} = \frac{12+4i }{8} = \frac{3}{2} - \frac{-1}{2}i \)