Giả sử  $w=x+yi(x,y\in R)$

$w=2z+1-i\Rightarrow z=\frac{w-1+i}{2}=\frac{x+yi-1+i}{2}=\frac{(x-1)+(y+10i}{2}$

$\left| z-3+4i \right|=2\Leftrightarrow \left| \frac{(x-1)+(y+1)i}{2}-3+4i \right|=2$

$\Leftrightarrow \left| \frac{x-7+(y+9)i}{2} \right|=2$   

$\Leftrightarrow \sqrt{{{\left( \frac{x-7}{2} \right)}^{2}}+{{\left( \frac{y+9}{2} \right)}^{2}}}=2$

$\Leftrightarrow {{\left( x-7 \right)}^{2}}+{{\left( y+9 \right)}^{2}}=16$