Xét các số phức ${{z}, {w}}$ thỏa mãn ${\mid {z}=1}$ và...

Ta có ${|{z}+{i} \overline{{w}}+6-{8i}| \geq|6-8 {i}|-|{z}|-|{i} \overline{{w}}|=10-1-2=7}$

Dấu " " " xảy ra khi

$\left\{ \begin{array}{*{35}{l}}

z=t(6-8i) \\

\begin{matrix}

i\bar{w}={t}'(6-8i),\forall t,{t}'\le 0 \\

|z|=1,|w|=2 \\

\end{matrix} \\

\end{array}\Leftrightarrow \left\{ \begin{array}{*{35}{l}}

z=-\dfrac{1}{10}(6-8i) \\

i\bar{w}=-\dfrac{2}{10}(6-8i) \\

\end{array}\Leftrightarrow \left\{ \begin{array}{*{35}{l}}

z=-\dfrac{1}{10}(6-8i) \\

\bar{w}=\dfrac{1}{5}(8+6i) \\

\end{array}\Leftrightarrow \left\{ \begin{matrix}

z=-\dfrac{1}{10}(6-8i) \\

w=\dfrac{1}{5}(8-6i) \\

\end{matrix} \right. \right. \right. \right.$

${{Khi}}$ đó ${|{Z}-{w}|=\dfrac{\sqrt{221}}{5}}$