Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \(\frac{3+3i}{1-3i}= \frac{3+3i}{1-3i} \cdot \frac{1+3i}{1+3i} = \frac{3+9i +3 i+9i^2 }{(1)^2-(-3i)^2} = \frac{3+9i +3 i-9}{1 + 9} = \frac{-6+12i }{10} = \frac{-3}{5} - \frac{-6}{5}i \)
2. \((6-3i) \cdot (1+i)= 6+6i -3 i-3i^2 = 6+6i -3 i+3= \color{red}{6+3}\color{blue}{+6i -3i}=\color{red}{9}\color{blue}{+3i}\)
3. \((5-4i) \cdot (6+10i)= 30+50i -24 i-40i^2 = 30+50i -24 i+40= \color{red}{30+40}\color{blue}{+50i -24i}=\color{red}{70}\color{blue}{+26i}\)
4. \(\frac{-8-10i}{8+4i}= \frac{-8-10i}{8+4i} \cdot \frac{8-4i}{8-4i} = \frac{-64+32i -80 i+40i^2 }{(8)^2-(4i)^2} = \frac{-64+32i -80 i-40}{64 + 16} = \frac{-104-48i }{80} = \frac{-13}{10} + \frac{-3}{5}i \)
5. \((-10-8i)\cdot (+9i)= -90 i-72i^2 = \color{red}{72}\color{blue}{-90i}\)
6. \((9-2i)\cdot (-9i)= -81 i+18i^2 = \color{red}{-18}\color{blue}{-81i}\)
7. \((-3-i) \cdot (10-10i)= -30+30i -10 i+10i^2 = -30+30i -10 i-10= \color{red}{-30-10}\color{blue}{+30i -10i}=\color{red}{-40}\color{blue}{+20i}\)
8. \((-1+5i)\cdot (-4i)= +4 i-20i^2 = \color{red}{20}\color{blue}{+4i}\)
9. \((3-6i) \cdot (9+2i)= 27+6i -54 i-12i^2 = 27+6i -54 i+12= \color{red}{27+12}\color{blue}{+6i -54i}=\color{red}{39}\color{blue}{-48i}\)
10. \((-8+5i) \cdot (-3+4i)= 24-32i -15 i+20i^2 = 24-32i -15 i-20= \color{red}{24-20}\color{blue}{-32i -15i}=\color{red}{4}\color{blue}{-47i}\)
11. \((-9+4i)\cdot (-7i)= +63 i-28i^2 = \color{red}{28}\color{blue}{+63i}\)
12. \((3+6i) \cdot (5+3i)= 15+9i +30 i+18i^2 = 15+9i +30 i-18= \color{red}{15-18}\color{blue}{+9i +30i}=\color{red}{-3}\color{blue}{+39i}\)