Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-5+9i) \cdot (2+7i)= -10-35i +18 i+63i^2 = -10-35i +18 i-63= \color{red}{-10-63}\color{blue}{-35i +18i}=\color{red}{-73}\color{blue}{-17i}\)
2. \((10-10i) \cdot (-2+2i)= -20+20i +20 i-20i^2 = -20+20i +20 i+20= \color{red}{-20+20}\color{blue}{+20i +20i}=\color{blue}{40i}\)
3. \(\frac{10+4i}{1-4i}= \frac{10+4i}{1-4i} \cdot \frac{1+4i}{1+4i} = \frac{10+40i +4 i+16i^2 }{(1)^2-(-4i)^2} = \frac{10+40i +4 i-16}{1 + 16} = \frac{-6+44i }{17} = \frac{-6}{17} - \frac{-44}{17}i \)
4. \((8-i) \cdot (-3+6i)= -24+48i +3 i-6i^2 = -24+48i +3 i+6= \color{red}{-24+6}\color{blue}{+48i +3i}=\color{red}{-18}\color{blue}{+51i}\)
5. \((+6i) \cdot (9-8i)= +54 i-48i^2 = \color{red}{48}\color{blue}{+54i}\)
6. \(\frac{-3+6i}{3+9i}= \frac{-3+6i}{3+9i} \cdot \frac{3-9i}{3-9i} = \frac{-9+27i +18 i-54i^2 }{(3)^2-(9i)^2} = \frac{-9+27i +18 i+54}{9 + 81} = \frac{45+45i }{90} = \frac{1}{2} - \frac{-1}{2}i \)
7. \((4+3i)\cdot (+i)= +4 i+3i^2 = \color{red}{-3}\color{blue}{+4i}\)
8. \((4-7i) \cdot (-5-10i)= -20-40i +35 i+70i^2 = -20-40i +35 i-70= \color{red}{-20-70}\color{blue}{-40i +35i}=\color{red}{-90}\color{blue}{-5i}\)
9. \((-3i) \cdot (7-4i)= -21 i+12i^2 = \color{red}{-12}\color{blue}{-21i}\)
10. \((-5i) \cdot (-7+5i)= +35 i-25i^2 = \color{red}{25}\color{blue}{+35i}\)
11. \((-3+10i) \cdot (4-i)= -12+3i +40 i-10i^2 = -12+3i +40 i+10= \color{red}{-12+10}\color{blue}{+3i +40i}=\color{red}{-2}\color{blue}{+43i}\)
12. \((-5+8i) \cdot (-6-7i)= 30+35i -48 i-56i^2 = 30+35i -48 i+56= \color{red}{30+56}\color{blue}{+35i -48i}=\color{red}{86}\color{blue}{-13i}\)