Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-3+i) \cdot (-7-3i)= 21+9i -7 i-3i^2 = 21+9i -7 i+3= \color{red}{21+3}\color{blue}{+9i -7i}=\color{red}{24}\color{blue}{+2i}\)
2. \(\frac{4+3i}{10-9i}= \frac{4+3i}{10-9i} \cdot \frac{10+9i}{10+9i} = \frac{40+36i +30 i+27i^2 }{(10)^2-(-9i)^2} = \frac{40+36i +30 i-27}{100 + 81} = \frac{13+66i }{181} = \frac{13}{181} - \frac{-66}{181}i \)
3. \(\frac{3+9i}{3+6i}= \frac{3+9i}{3+6i} \cdot \frac{3-6i}{3-6i} = \frac{9-18i +27 i-54i^2 }{(3)^2-(6i)^2} = \frac{9-18i +27 i+54}{9 + 36} = \frac{63+9i }{45} = \frac{7}{5} - \frac{-1}{5}i \)
4. \((-8i) \cdot (-7+7i)= +56 i-56i^2 = \color{red}{56}\color{blue}{+56i}\)
5. \((+4i) \cdot (-2-8i)= -8 i-32i^2 = \color{red}{32}\color{blue}{-8i}\)
6. \((-4i) \cdot (3+2i)= -12 i-8i^2 = \color{red}{8}\color{blue}{-12i}\)
7. \((-2i) \cdot (3+8i)= -6 i-16i^2 = \color{red}{16}\color{blue}{-6i}\)
8. \((+3i) \cdot (-8+8i)= -24 i+24i^2 = \color{red}{-24}\color{blue}{-24i}\)
9. \((-3-6i)\cdot (+7i)= -21 i-42i^2 = \color{red}{42}\color{blue}{-21i}\)
10. \((4+9i)\cdot (-i)= -4 i-9i^2 = \color{red}{9}\color{blue}{-4i}\)
11. \((-1-3i) \cdot (-3-8i)= 3+8i +9 i+24i^2 = 3+8i +9 i-24= \color{red}{3-24}\color{blue}{+8i +9i}=\color{red}{-21}\color{blue}{+17i}\)
12. \(\frac{-5-10i}{5+6i}= \frac{-5-10i}{5+6i} \cdot \frac{5-6i}{5-6i} = \frac{-25+30i -50 i+60i^2 }{(5)^2-(6i)^2} = \frac{-25+30i -50 i-60}{25 + 36} = \frac{-85-20i }{61} = \frac{-85}{61} + \frac{-20}{61}i \)