Question

me ajudem por favor




Obtenha o número complexo z tal que Z = 5/1+2i + 5i/1-2i - i+2/-1+2i

Answer 1

$z=\frac{5}{1+2i} + \frac {5i}{1-2i} - \frac{i+2}{-1+2i}\\\\ z=(\frac{5}{1+2i}\cdot\frac{1-2i}{1-2i}) + (\frac {5i}{1-2i} \cdot\frac {1+2i}{1+2i}) - (\frac{i+2}{-1+2i}\cdot\frac{-1-2i}{-1-2i})\\\\ z=(\frac{5-10i}{1-2i+2i-4i^2})+(\frac{5i+10i^2}{1+2i-2i-4i^2})-(\frac{-i-2i^2-2-4i}{1+2i-2i-4i^2})\\\\z=(\frac{5-10i}{5})+(\frac{-10+5i}{5})-(\frac{-5i}{5})\\\\ z=(1-2i)+(-2+i)-(-i)\\\\z=-1$