Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-9i) \cdot (6+2i)= -54 i-18i^2 = \color{red}{18}\color{blue}{-54i}\)
2. \(\frac{2-4i}{7-2i}= \frac{2-4i}{7-2i} \cdot \frac{7+2i}{7+2i} = \frac{14+4i -28 i-8i^2 }{(7)^2-(-2i)^2} = \frac{14+4i -28 i+8}{49 + 4} = \frac{22-24i }{53} = \frac{22}{53} + \frac{-24}{53}i \)
3. \((+8i) \cdot (3-7i)= +24 i-56i^2 = \color{red}{56}\color{blue}{+24i}\)
4. \(\frac{-7-9i}{-1-9i}= \frac{-7-9i}{-1-9i} \cdot \frac{-1+9i}{-1+9i} = \frac{7-63i +9 i-81i^2 }{(-1)^2-(-9i)^2} = \frac{7-63i +9 i+81}{1 + 81} = \frac{88-54i }{82} = \frac{44}{41} + \frac{-27}{41}i \)
5. \(\frac{-9-9i}{-7+6i}= \frac{-9-9i}{-7+6i} \cdot \frac{-7-6i}{-7-6i} = \frac{63+54i +63 i+54i^2 }{(-7)^2-(6i)^2} = \frac{63+54i +63 i-54}{49 + 36} = \frac{9+117i }{85} = \frac{9}{85} - \frac{-117}{85}i \)
6. \(\frac{9+4i}{8-8i}= \frac{9+4i}{8-8i} \cdot \frac{8+8i}{8+8i} = \frac{72+72i +32 i+32i^2 }{(8)^2-(-8i)^2} = \frac{72+72i +32 i-32}{64 + 64} = \frac{40+104i }{128} = \frac{5}{16} - \frac{-13}{16}i \)
7. \(\frac{-5-9i}{-3-7i}= \frac{-5-9i}{-3-7i} \cdot \frac{-3+7i}{-3+7i} = \frac{15-35i +27 i-63i^2 }{(-3)^2-(-7i)^2} = \frac{15-35i +27 i+63}{9 + 49} = \frac{78-8i }{58} = \frac{39}{29} + \frac{-4}{29}i \)
8. \(\frac{4+3i}{-1+6i}= \frac{4+3i}{-1+6i} \cdot \frac{-1-6i}{-1-6i} = \frac{-4-24i -3 i-18i^2 }{(-1)^2-(6i)^2} = \frac{-4-24i -3 i+18}{1 + 36} = \frac{14-27i }{37} = \frac{14}{37} + \frac{-27}{37}i \)
9. \((-4+6i) \cdot (6+4i)= -24-16i +36 i+24i^2 = -24-16i +36 i-24= \color{red}{-24-24}\color{blue}{-16i +36i}=\color{red}{-48}\color{blue}{+20i}\)
10. \((-1-9i) \cdot (-4-4i)= 4+4i +36 i+36i^2 = 4+4i +36 i-36= \color{red}{4-36}\color{blue}{+4i +36i}=\color{red}{-32}\color{blue}{+40i}\)
11. \(\frac{4-6i}{7+3i}= \frac{4-6i}{7+3i} \cdot \frac{7-3i}{7-3i} = \frac{28-12i -42 i+18i^2 }{(7)^2-(3i)^2} = \frac{28-12i -42 i-18}{49 + 9} = \frac{10-54i }{58} = \frac{5}{29} + \frac{-27}{29}i \)
12. \(\frac{-1+5i}{-4-9i}= \frac{-1+5i}{-4-9i} \cdot \frac{-4+9i}{-4+9i} = \frac{4-9i -20 i+45i^2 }{(-4)^2-(-9i)^2} = \frac{4-9i -20 i-45}{16 + 81} = \frac{-41-29i }{97} = \frac{-41}{97} + \frac{-29}{97}i \)