Đặt \(z=x+yi\Rightarrow\left|x-3+\left(y-1\right)i\right|=\left|x+\left(y+1\right)i\right|\)
\(\Rightarrow\left(x-3\right)^2+\left(y-1\right)^2=x^2+\left(y+1\right)^2\)
\(\Rightarrow6x+4y-9=0\Rightarrow y=\dfrac{9-6x}{4}\)
\(P=\left|\left(x-1\right)+\left(y+3\right)i\right|=\sqrt{\left(x-1\right)^2+\left(y+3\right)^2}\)
\(=\sqrt{\left(x-1\right)^2+\left(\dfrac{9-6x}{4}+3\right)^2}=\sqrt{\dfrac{13}{4}\left(x-\dfrac{71}{26}\right)^2+\dfrac{225}{52}}\ge\sqrt{\dfrac{225}{52}}\)
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