Question

verifique se (a) Re(-i(2 - 3i)2) = -12

Answer 1

Correto.

$Re\,\left(-i\,.\,(2-3i)^2\,\right)~=\\\\\\=~Re\,\left(-i\,.\,(2-3i).(2-3i)\,\right)\\\\\\=~Re\,\left(-i\,.\,(\,2\,.\,2~+~2\,.\,(-3i)~+~(-3i)\,.\,2)~+~(-3i)\,.\,(-3i)\,)~\right)\\\\\\=~Re\,\left(-i\,.\,(\,4~-~6i~-~6i~+~9i^2\,)~\right)\\\\\\=~Re\,\left(-i\,.\,(\,4~-~12i~+~9\,.\,(-1)\,)~\right)\\\\\\=~Re\,\left(-i\,.\,(\,4~-~12i~-~9\,)~\right)\\\\\\=~Re\,\left(-i\,.\,(-5~-~12i\,)~\right)\\\\\\=~Re\,\left(~5i+12i^2~\right)\\\\\\=~Re\,\left(~5i~+~12\,.\,(-1)~\right)$

$=~Re\,\left(~5i~-~12~\right)\\\\\\=~\boxed{-12}$