✅ Após resolver os cálculos, concluímos que o valor do produto dos referidos número complexos é:
[tex]\Large\displaystyle\text{$\begin{gathered}\boxed{\boxed{\:\:\:\bf z_{1} \cdot z_{2} = -96 + 28i\:\:\:}}\end{gathered}$}[/tex]
Sejam os números complexos:
[tex]\Large\begin{cases} z_{1} = 11 + 2i\\z_{2} = -8 + 4i\end{cases}[/tex]
Calculando o produto dos números complexos:
[tex]\Large\displaystyle\text{$\begin{gathered} z_{1} \cdot z_{2} = (11 + 2i)\cdot(-8 + 4i)\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} = -88 - 16i + 44i + 8i^{2}\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} = -88 + 28i + 8i^{2}\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} = -88 + 28i + 8\cdot(-1)\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} = - 88 + 28i - 8\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} = - 96 + 28i\end{gathered}$}[/tex]
✅ Portanto, o valor do produto é:
[tex]\Large\displaystyle\text{$\begin{gathered} z_{1}\cdot z_{2} = -96 + 28i\end{gathered}$}[/tex]
[tex]\LARGE\displaystyle\text{$\begin{gathered} \underline{\boxed{\boldsymbol{\:\:\:Bons \:estudos!!\:\:\:Boa\: sorte!!\:\:\:}}}\end{gathered}$}[/tex]
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