Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \(\frac{-10+5i}{-1-7i}= \frac{-10+5i}{-1-7i} \cdot \frac{-1+7i}{-1+7i} = \frac{10-70i -5 i+35i^2 }{(-1)^2-(-7i)^2} = \frac{10-70i -5 i-35}{1 + 49} = \frac{-25-75i }{50} = \frac{-1}{2} + \frac{-3}{2}i \)
2. \((-8-8i) \cdot (1+9i)= -8-72i -8 i-72i^2 = -8-72i -8 i+72= \color{red}{-8+72}\color{blue}{-72i -8i}=\color{red}{64}\color{blue}{-80i}\)
3. \((2-5i) \cdot (-5-7i)= -10-14i +25 i+35i^2 = -10-14i +25 i-35= \color{red}{-10-35}\color{blue}{-14i +25i}=\color{red}{-45}\color{blue}{+11i}\)
4. \((-4+2i) \cdot (8-2i)= -32+8i +16 i-4i^2 = -32+8i +16 i+4= \color{red}{-32+4}\color{blue}{+8i +16i}=\color{red}{-28}\color{blue}{+24i}\)
5. \((-8-9i)\cdot (-5i)= +40 i+45i^2 = \color{red}{-45}\color{blue}{+40i}\)
6. \((+10i) \cdot (-5+6i)= -50 i+60i^2 = \color{red}{-60}\color{blue}{-50i}\)
7. \((7+9i) \cdot (2+8i)= 14+56i +18 i+72i^2 = 14+56i +18 i-72= \color{red}{14-72}\color{blue}{+56i +18i}=\color{red}{-58}\color{blue}{+74i}\)
8. \((6+9i) \cdot (-1+9i)= -6+54i -9 i+81i^2 = -6+54i -9 i-81= \color{red}{-6-81}\color{blue}{+54i -9i}=\color{red}{-87}\color{blue}{+45i}\)
9. \((9-7i) \cdot (-10+8i)= -90+72i +70 i-56i^2 = -90+72i +70 i+56= \color{red}{-90+56}\color{blue}{+72i +70i}=\color{red}{-34}\color{blue}{+142i}\)
10. \(\frac{10-4i}{5-i}= \frac{10-4i}{5-i} \cdot \frac{5+i}{5+i} = \frac{50+10i -20 i-4i^2 }{(5)^2-(-1i)^2} = \frac{50+10i -20 i+4}{25 + 1} = \frac{54-10i }{26} = \frac{27}{13} + \frac{-5}{13}i \)
11. \((-10i) \cdot (4+6i)= -40 i-60i^2 = \color{red}{60}\color{blue}{-40i}\)
12. \(\frac{-1-i}{-5+3i}= \frac{-1-i}{-5+3i} \cdot \frac{-5-3i}{-5-3i} = \frac{5+3i +5 i+3i^2 }{(-5)^2-(3i)^2} = \frac{5+3i +5 i-3}{25 + 9} = \frac{2+8i }{34} = \frac{1}{17} - \frac{-4}{17}i \)