Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((1+i) \cdot (-1+2i)= -1+2i -1 i+2i^2 = -1+2i -1 i-2= \color{red}{-1-2}\color{blue}{+2i -i}=\color{red}{-3}\color{blue}{+i}\)
2. \((-10i) \cdot (8+3i)= -80 i-30i^2 = \color{red}{30}\color{blue}{-80i}\)
3. \((3-2i) \cdot (-5-7i)= -15-21i +10 i+14i^2 = -15-21i +10 i-14= \color{red}{-15-14}\color{blue}{-21i +10i}=\color{red}{-29}\color{blue}{-11i}\)
4. \((4-8i) \cdot (-7+i)= -28+4i +56 i-8i^2 = -28+4i +56 i+8= \color{red}{-28+8}\color{blue}{+4i +56i}=\color{red}{-20}\color{blue}{+60i}\)
5. \((-3-2i) \cdot (4+10i)= -12-30i -8 i-20i^2 = -12-30i -8 i+20= \color{red}{-12+20}\color{blue}{-30i -8i}=\color{red}{8}\color{blue}{-38i}\)
6. \((10-4i)\cdot (-2i)= -20 i+8i^2 = \color{red}{-8}\color{blue}{-20i}\)
7. \((-6+3i) \cdot (-8+10i)= 48-60i -24 i+30i^2 = 48-60i -24 i-30= \color{red}{48-30}\color{blue}{-60i -24i}=\color{red}{18}\color{blue}{-84i}\)
8. \((-8+5i) \cdot (-4+4i)= 32-32i -20 i+20i^2 = 32-32i -20 i-20= \color{red}{32-20}\color{blue}{-32i -20i}=\color{red}{12}\color{blue}{-52i}\)
9. \(\frac{-1+2i}{9+4i}= \frac{-1+2i}{9+4i} \cdot \frac{9-4i}{9-4i} = \frac{-9+4i +18 i-8i^2 }{(9)^2-(4i)^2} = \frac{-9+4i +18 i+8}{81 + 16} = \frac{-1+22i }{97} = \frac{-1}{97} - \frac{-22}{97}i \)
10. \(\frac{7+2i}{3+10i}= \frac{7+2i}{3+10i} \cdot \frac{3-10i}{3-10i} = \frac{21-70i +6 i-20i^2 }{(3)^2-(10i)^2} = \frac{21-70i +6 i+20}{9 + 100} = \frac{41-64i }{109} = \frac{41}{109} + \frac{-64}{109}i \)
11. \((-9-2i) \cdot (5-8i)= -45+72i -10 i+16i^2 = -45+72i -10 i-16= \color{red}{-45-16}\color{blue}{+72i -10i}=\color{red}{-61}\color{blue}{+62i}\)
12. \((-4-3i) \cdot (3+7i)= -12-28i -9 i-21i^2 = -12-28i -9 i+21= \color{red}{-12+21}\color{blue}{-28i -9i}=\color{red}{9}\color{blue}{-37i}\)