Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-10-2i) \cdot (4+9i)= -40-90i -8 i-18i^2 = -40-90i -8 i+18= \color{red}{-40+18}\color{blue}{-90i -8i}=\color{red}{-22}\color{blue}{-98i}\)
2. \((8+9i) \cdot (-3+3i)= -24+24i -27 i+27i^2 = -24+24i -27 i-27= \color{red}{-24-27}\color{blue}{+24i -27i}=\color{red}{-51}\color{blue}{-3i}\)
3. \(\frac{-8+9i}{-9-9i}= \frac{-8+9i}{-9-9i} \cdot \frac{-9+9i}{-9+9i} = \frac{72-72i -81 i+81i^2 }{(-9)^2-(-9i)^2} = \frac{72-72i -81 i-81}{81 + 81} = \frac{-9-153i }{162} = \frac{-1}{18} + \frac{-17}{18}i \)
4. \((+5i) \cdot (9-3i)= +45 i-15i^2 = \color{red}{15}\color{blue}{+45i}\)
5. \((-9-5i) \cdot (2-4i)= -18+36i -10 i+20i^2 = -18+36i -10 i-20= \color{red}{-18-20}\color{blue}{+36i -10i}=\color{red}{-38}\color{blue}{+26i}\)
6. \((+10i) \cdot (4+i)= +40 i+10i^2 = \color{red}{-10}\color{blue}{+40i}\)
7. \((-1-2i) \cdot (-9+9i)= 9-9i +18 i-18i^2 = 9-9i +18 i+18= \color{red}{9+18}\color{blue}{-9i +18i}=\color{red}{27}\color{blue}{+9i}\)
8. \(\frac{7-10i}{1-8i}= \frac{7-10i}{1-8i} \cdot \frac{1+8i}{1+8i} = \frac{7+56i -10 i-80i^2 }{(1)^2-(-8i)^2} = \frac{7+56i -10 i+80}{1 + 64} = \frac{87+46i }{65} = \frac{87}{65} - \frac{-46}{65}i \)
9. \((10-3i)\cdot (+6i)= +60 i-18i^2 = \color{red}{18}\color{blue}{+60i}\)
10. \((-1-5i) \cdot (9+5i)= -9-5i -45 i-25i^2 = -9-5i -45 i+25= \color{red}{-9+25}\color{blue}{-5i -45i}=\color{red}{16}\color{blue}{-50i}\)
11. \(\frac{3-i}{-7-10i}= \frac{3-i}{-7-10i} \cdot \frac{-7+10i}{-7+10i} = \frac{-21+30i +7 i-10i^2 }{(-7)^2-(-10i)^2} = \frac{-21+30i +7 i+10}{49 + 100} = \frac{-11+37i }{149} = \frac{-11}{149} - \frac{-37}{149}i \)
12. \(\frac{-4-6i}{-3-8i}= \frac{-4-6i}{-3-8i} \cdot \frac{-3+8i}{-3+8i} = \frac{12-32i +18 i-48i^2 }{(-3)^2-(-8i)^2} = \frac{12-32i +18 i+48}{9 + 64} = \frac{60-14i }{73} = \frac{60}{73} + \frac{-14}{73}i \)