Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((+10i) \cdot (-6+5i)= -60 i+50i^2 = \color{red}{-50}\color{blue}{-60i}\)
2. \(\frac{9+7i}{-3+2i}= \frac{9+7i}{-3+2i} \cdot \frac{-3-2i}{-3-2i} = \frac{-27-18i -21 i-14i^2 }{(-3)^2-(2i)^2} = \frac{-27-18i -21 i+14}{9 + 4} = \frac{-13-39i }{13} = -1+ 3i\)
3. \((-9-8i) \cdot (8-3i)= -72+27i -64 i+24i^2 = -72+27i -64 i-24= \color{red}{-72-24}\color{blue}{+27i -64i}=\color{red}{-96}\color{blue}{-37i}\)
4. \((+4i) \cdot (-8+i)= -32 i+4i^2 = \color{red}{-4}\color{blue}{-32i}\)
5. \((10-2i) \cdot (-4-i)= -40-10i +8 i+2i^2 = -40-10i +8 i-2= \color{red}{-40-2}\color{blue}{-10i +8i}=\color{red}{-42}\color{blue}{-2i}\)
6. \(\frac{-4-7i}{10+4i}= \frac{-4-7i}{10+4i} \cdot \frac{10-4i}{10-4i} = \frac{-40+16i -70 i+28i^2 }{(10)^2-(4i)^2} = \frac{-40+16i -70 i-28}{100 + 16} = \frac{-68-54i }{116} = \frac{-17}{29} + \frac{-27}{58}i \)
7. \(\frac{9-7i}{8+4i}= \frac{9-7i}{8+4i} \cdot \frac{8-4i}{8-4i} = \frac{72-36i -56 i+28i^2 }{(8)^2-(4i)^2} = \frac{72-36i -56 i-28}{64 + 16} = \frac{44-92i }{80} = \frac{11}{20} + \frac{-23}{20}i \)
8. \(\frac{-9+8i}{10-9i}= \frac{-9+8i}{10-9i} \cdot \frac{10+9i}{10+9i} = \frac{-90-81i +80 i+72i^2 }{(10)^2-(-9i)^2} = \frac{-90-81i +80 i-72}{100 + 81} = \frac{-162-i }{181} = \frac{-162}{181} + \frac{-1}{181}i \)
9. \(\frac{5+8i}{4-9i}= \frac{5+8i}{4-9i} \cdot \frac{4+9i}{4+9i} = \frac{20+45i +32 i+72i^2 }{(4)^2-(-9i)^2} = \frac{20+45i +32 i-72}{16 + 81} = \frac{-52+77i }{97} = \frac{-52}{97} - \frac{-77}{97}i \)
10. \((-9-7i) \cdot (10-4i)= -90+36i -70 i+28i^2 = -90+36i -70 i-28= \color{red}{-90-28}\color{blue}{+36i -70i}=\color{red}{-118}\color{blue}{-34i}\)
11. \(\frac{-10+9i}{8+6i}= \frac{-10+9i}{8+6i} \cdot \frac{8-6i}{8-6i} = \frac{-80+60i +72 i-54i^2 }{(8)^2-(6i)^2} = \frac{-80+60i +72 i+54}{64 + 36} = \frac{-26+132i }{100} = \frac{-13}{50} - \frac{-33}{25}i \)
12. \((-7-9i)\cdot (-6i)= +42 i+54i^2 = \color{red}{-54}\color{blue}{+42i}\)