Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-7-2i) \cdot (-5+10i)= 35-70i +10 i-20i^2 = 35-70i +10 i+20= \color{red}{35+20}\color{blue}{-70i +10i}=\color{red}{55}\color{blue}{-60i}\)
2. \((4-3i) \cdot (-10+2i)= -40+8i +30 i-6i^2 = -40+8i +30 i+6= \color{red}{-40+6}\color{blue}{+8i +30i}=\color{red}{-34}\color{blue}{+38i}\)
3. \(\frac{-10-9i}{-3+9i}= \frac{-10-9i}{-3+9i} \cdot \frac{-3-9i}{-3-9i} = \frac{30+90i +27 i+81i^2 }{(-3)^2-(9i)^2} = \frac{30+90i +27 i-81}{9 + 81} = \frac{-51+117i }{90} = \frac{-17}{30} - \frac{-13}{10}i \)
4. \((+6i) \cdot (-4+6i)= -24 i+36i^2 = \color{red}{-36}\color{blue}{-24i}\)
5. \(\frac{8-7i}{3+9i}= \frac{8-7i}{3+9i} \cdot \frac{3-9i}{3-9i} = \frac{24-72i -21 i+63i^2 }{(3)^2-(9i)^2} = \frac{24-72i -21 i-63}{9 + 81} = \frac{-39-93i }{90} = \frac{-13}{30} + \frac{-31}{30}i \)
6. \((-10i) \cdot (7+9i)= -70 i-90i^2 = \color{red}{90}\color{blue}{-70i}\)
7. \((6-4i) \cdot (10+9i)= 60+54i -40 i-36i^2 = 60+54i -40 i+36= \color{red}{60+36}\color{blue}{+54i -40i}=\color{red}{96}\color{blue}{+14i}\)
8. \((-9i) \cdot (3-9i)= -27 i+81i^2 = \color{red}{-81}\color{blue}{-27i}\)
9. \(\frac{9+i}{4+2i}= \frac{9+i}{4+2i} \cdot \frac{4-2i}{4-2i} = \frac{36-18i +4 i-2i^2 }{(4)^2-(2i)^2} = \frac{36-18i +4 i+2}{16 + 4} = \frac{38-14i }{20} = \frac{19}{10} + \frac{-7}{10}i \)
10. \((5+5i) \cdot (-2-4i)= -10-20i -10 i-20i^2 = -10-20i -10 i+20= \color{red}{-10+20}\color{blue}{-20i -10i}=\color{red}{10}\color{blue}{-30i}\)
11. \((+5i) \cdot (9+2i)= +45 i+10i^2 = \color{red}{-10}\color{blue}{+45i}\)
12. \(\frac{-2+9i}{-3-5i}= \frac{-2+9i}{-3-5i} \cdot \frac{-3+5i}{-3+5i} = \frac{6-10i -27 i+45i^2 }{(-3)^2-(-5i)^2} = \frac{6-10i -27 i-45}{9 + 25} = \frac{-39-37i }{34} = \frac{-39}{34} + \frac{-37}{34}i \)