Question

Calcule a e b de modo que os números complexos Z = (a+b) + (a-b)i e W = 8 + 2i sejam iguais.

Answer 1

$\Large\boxed{\begin{array}{l}\sf Z=(a+b)+(a-b)i~~W=8+2i\\\sf Z=W\iff\begin{cases}\sf a+b=8\\\sf a-b=2\end{cases}\\+\underline{\begin{cases}\sf a+\backslash\!\!\!b=8\\\sf a-\backslash\!\!\!b=2\end{cases}}\\\sf 2a=10\\\sf a=\dfrac{10}{2}\\\\\sf a=5\\\sf a+b=8\\\sf 5+b=8\\\sf b=8-5\\\sf b=3\end{array}}$