Question

Determine o número complexo z tal que 5z + iz = 2+4i

Answer 1

$5z+iz=2+4i\\\\\\ \dfrac{5z+iz}{5+i} = \dfrac{2+4i}{5+i} \\\\\\ \dfrac{z(5+i)}{5+i} = \dfrac{(2+4i)(5-i)}{(5+i)(5-i)}\\\\\\ z = \dfrac{(2\cdot \:5-4(-1))+(2(-1)+4\cdot \:5)i}{5^2+1^2} \\\\\\ z = \dfrac{14+18i}{26} \Rightarrow z = \dfrac{2(7+9i)}{26}\\\\\\ z= \dfrac{7+9i}{13} \\\\\\ z = \dfrac{7}{13}+\dfrac{9}{13}i$