Xét các số phức ${z=4-2 i}$ thỏa mãn ${x>0}$ và ${\log _2(5 x)=3...

Do ${|w|=2}$ nên ${|\overrightarrow{i w}|=|i w|=|i| \cdot|w|=2}$.
${
\text { Ta có: }|z+\overline{i w}+6+8 i| \geq|6+8 i|-|z|-|\overrightarrow{i w}|=7 \text { . }
}$
Dấu bằng xảy ra $\left\{ \begin{array}{*{35}{l}}
z=k(6+8i)(k<0) \\
\overline{iw}=m(6+8i)(m<0) \\
|z|=1 \\
|\overrightarrow{iw}|=2 \\
\end{array}\Leftrightarrow \left\{ \begin{array}{*{35}{l}}
k=-\dfrac{1}{10} \\
m=-\dfrac{1}{5} \\
z=-\dfrac{3}{5}-\dfrac{4}{5}i \\
\overline{iw}=-\dfrac{6}{5}-\dfrac{8}{5}i \\
\end{array}\Leftrightarrow \left\{ \begin{array}{*{35}{l}}
k=-\dfrac{1}{10} \\
m=-\dfrac{1}{5} \\
z=-\dfrac{3}{5}-\dfrac{4}{5}i \\
w=\dfrac{8}{5}+\dfrac{6}{5}i \\
\end{array} \right. \right. \right.$
Khi đó ${|z-w|=\left|-\dfrac{3}{5}-\dfrac{4}{5} i-\dfrac{8}{5}-\dfrac{6}{5} i\right|=\dfrac{\sqrt{221}}{5}}$