Question

Calcule o módulo do número complexo
Z=(2+2i).(1-i)

Mande o cálculo em anexo (foto)

Answer 1

$Z=2(1+i)(1-i)\\ \\ Z=2(2)\\ \\Z=4\Longrightarrow \boxed{|Z|=4}$

Answer 2

✅ Finalizando os cálculos, concluímos que o módulo do referido número complexo é:

      $\Large\displaystyle\text{ \begin{gathered}\boxed{\boxed{\:\:\:\bf |z| = 4\:u\cdot c\:\:\:}}\end{gathered} }$

Resolvendo o produto do número complexo:

     $\Large\displaystyle\begin{gathered} z = (2 + 2i)\cdot(1 - i)\end{gathered}$

         $\Large\displaystyle\begin{gathered}= 2 + 2i - 2i -2i^{2} \end{gathered}$

         $\Large\displaystyle\begin{gathered} = 2 - 2\cdot(-1)\end{gathered}$

         $\Large\displaystyle\begin{gathered} = 2 + 2\end{gathered}$

         $\Large\displaystyle\begin{gathered} = 4\end{gathered}$

Portanto:

     $\Large\displaystyle\begin{gathered}z = 4 \end{gathered}$

Então, temos:

     $\Large\displaystyle\text{ \begin{gathered}|z| = \sqrt{4^{2} + 0^{2}} \end{gathered} }$

            $\Large\displaystyle\begin{gathered}= \sqrt{16} \end{gathered}$

            $\Large\displaystyle\begin{gathered} = 4\end{gathered}$

✅ Portanto, o módulo do número complexo é:

      $\Large\displaystyle\begin{gathered}|z| = 4\:u\cdot c \end{gathered}$

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