Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((+9i) \cdot (4-4i)= +36 i-36i^2 = \color{red}{36}\color{blue}{+36i}\)
2. \(\frac{4-2i}{-3+6i}= \frac{4-2i}{-3+6i} \cdot \frac{-3-6i}{-3-6i} = \frac{-12-24i +6 i+12i^2 }{(-3)^2-(6i)^2} = \frac{-12-24i +6 i-12}{9 + 36} = \frac{-24-18i }{45} = \frac{-8}{15} + \frac{-2}{5}i \)
3. \(\frac{8-2i}{3+9i}= \frac{8-2i}{3+9i} \cdot \frac{3-9i}{3-9i} = \frac{24-72i -6 i+18i^2 }{(3)^2-(9i)^2} = \frac{24-72i -6 i-18}{9 + 81} = \frac{6-78i }{90} = \frac{1}{15} + \frac{-13}{15}i \)
4. \((4-i)\cdot (+5i)= +20 i-5i^2 = \color{red}{5}\color{blue}{+20i}\)
5. \(\frac{5+8i}{-8-9i}= \frac{5+8i}{-8-9i} \cdot \frac{-8+9i}{-8+9i} = \frac{-40+45i -64 i+72i^2 }{(-8)^2-(-9i)^2} = \frac{-40+45i -64 i-72}{64 + 81} = \frac{-112-19i }{145} = \frac{-112}{145} + \frac{-19}{145}i \)
6. \(\frac{-8+7i}{1+4i}= \frac{-8+7i}{1+4i} \cdot \frac{1-4i}{1-4i} = \frac{-8+32i +7 i-28i^2 }{(1)^2-(4i)^2} = \frac{-8+32i +7 i+28}{1 + 16} = \frac{20+39i }{17} = \frac{20}{17} - \frac{-39}{17}i \)
7. \(\frac{-4+9i}{-6-i}= \frac{-4+9i}{-6-i} \cdot \frac{-6+i}{-6+i} = \frac{24-4i -54 i+9i^2 }{(-6)^2-(-1i)^2} = \frac{24-4i -54 i-9}{36 + 1} = \frac{15-58i }{37} = \frac{15}{37} + \frac{-58}{37}i \)
8. \((1-i) \cdot (-3+2i)= -3+2i +3 i-2i^2 = -3+2i +3 i+2= \color{red}{-3+2}\color{blue}{+2i +3i}=\color{red}{-1}\color{blue}{+5i}\)
9. \((+9i) \cdot (-3+2i)= -27 i+18i^2 = \color{red}{-18}\color{blue}{-27i}\)
10. \((2-8i)\cdot (+5i)= +10 i-40i^2 = \color{red}{40}\color{blue}{+10i}\)
11. \((-8+3i) \cdot (-9-2i)= 72+16i -27 i-6i^2 = 72+16i -27 i+6= \color{red}{72+6}\color{blue}{+16i -27i}=\color{red}{78}\color{blue}{-11i}\)
12. \(\frac{-9+3i}{-4-9i}= \frac{-9+3i}{-4-9i} \cdot \frac{-4+9i}{-4+9i} = \frac{36-81i -12 i+27i^2 }{(-4)^2-(-9i)^2} = \frac{36-81i -12 i-27}{16 + 81} = \frac{9-93i }{97} = \frac{9}{97} + \frac{-93}{97}i \)