Question

Determinar o complexo z que satisfaz a igualdade seguinte 2z+5z=7+6i

Answer 1

$\large\boxed{\begin{array}{l}\rm z=a+bi\\\rm 2z+5z=7+6i\\\rm 2(a+bi)+5\cdot(a+bi)=7+6i\\\rm 2a+2bi+5a+5bi=7+6i\\\rm7a+7bi=7+6i\\\rm 7a=7\\\rm a=\dfrac{7}{7}\\\\\rm a=1\\\rm 7b=6\\\rm b=\dfrac{6}{7}\\\\\huge\boxed{\boxed{\boxed{\boxed{\rm z=1+\dfrac{6}{7}\,i}}}}\end{array}}$