Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \(\frac{10-6i}{2-2i}= \frac{10-6i}{2-2i} \cdot \frac{2+2i}{2+2i} = \frac{20+20i -12 i-12i^2 }{(2)^2-(-2i)^2} = \frac{20+20i -12 i+12}{4 + 4} = \frac{32+8i }{8} = 4- -1i\)
2. \((+10i) \cdot (-10-9i)= -100 i-90i^2 = \color{red}{90}\color{blue}{-100i}\)
3. \((6+10i) \cdot (6+2i)= 36+12i +60 i+20i^2 = 36+12i +60 i-20= \color{red}{36-20}\color{blue}{+12i +60i}=\color{red}{16}\color{blue}{+72i}\)
4. \(\frac{-1-5i}{6+5i}= \frac{-1-5i}{6+5i} \cdot \frac{6-5i}{6-5i} = \frac{-6+5i -30 i+25i^2 }{(6)^2-(5i)^2} = \frac{-6+5i -30 i-25}{36 + 25} = \frac{-31-25i }{61} = \frac{-31}{61} + \frac{-25}{61}i \)
5. \((4-7i) \cdot (-6+8i)= -24+32i +42 i-56i^2 = -24+32i +42 i+56= \color{red}{-24+56}\color{blue}{+32i +42i}=\color{red}{32}\color{blue}{+74i}\)
6. \((-i) \cdot (-5-5i)= +5 i+5i^2 = \color{red}{-5}\color{blue}{+5i}\)
7. \((-4i) \cdot (10-2i)= -40 i+8i^2 = \color{red}{-8}\color{blue}{-40i}\)
8. \((-1+10i) \cdot (-9+2i)= 9-2i -90 i+20i^2 = 9-2i -90 i-20= \color{red}{9-20}\color{blue}{-2i -90i}=\color{red}{-11}\color{blue}{-92i}\)
9. \((1-5i) \cdot (-5+5i)= -5+5i +25 i-25i^2 = -5+5i +25 i+25= \color{red}{-5+25}\color{blue}{+5i +25i}=\color{red}{20}\color{blue}{+30i}\)
10. \((-3-3i) \cdot (-1-5i)= 3+15i +3 i+15i^2 = 3+15i +3 i-15= \color{red}{3-15}\color{blue}{+15i +3i}=\color{red}{-12}\color{blue}{+18i}\)
11. \((4-6i)\cdot (-4i)= -16 i+24i^2 = \color{red}{-24}\color{blue}{-16i}\)
12. \((+10i) \cdot (-3-10i)= -30 i-100i^2 = \color{red}{100}\color{blue}{-30i}\)