Question

O número complexo z, tal que 5z + i = 12 + 6i, então 2z é?

Answer 1

$5Z~+~i~=~12~+~6i\\\\\\5Z~=~12~+~6i~-~i\\\\\\5Z~=~12~+~5i\\\\\\Z~=~\frac{12~+~5i}{5}\\\\\\\boxed{Z~=~\frac{12}{5}~+~i}$

Calculando agora 2Z:

$2Z~=~2~.~\left(\frac{12}{5}~+~i\right)\\\\\\2Z~=~\frac{2~.~12}{5}~+~2~.~i\\\\\\\boxed{2Z~=~\frac{24}{5}~+~2i~~~~ou~~~~4,8+2i}$