Cho các số phức $z,w$ thỏa mãn $\left| z-i \right|=2$ và $\left|...

Ta có:
Dấu “=” xảy ra khi:
$ \Leftrightarrow \left\{ \begin{aligned}
& z-i=\dfrac{2}{5}\left( 3+4i \right) \\
& \overline{w}-2=\dfrac{1}{5}\left( 3+4i \right) \\
\end{aligned} \right.$$\Leftrightarrow \left\{ \begin{aligned}
& z=\dfrac{6}{5}+\dfrac{13}{5}i \\
& \overline{w}=\dfrac{13}{5}+\dfrac{4}{5}i \\
\end{aligned} \right. \Leftrightarrow \left\{ \begin{aligned}
& z=\dfrac{6}{5}+\dfrac{13}{5}i \\
& w=\dfrac{13}{5}-\dfrac{4}{5}i \\
\end{aligned} \right.\left| z-w+1-\dfrac{12}{5}i \right|=\left| -\dfrac{2}{5}+i \right|=\dfrac{\sqrt{29}}{5}$.