4. If Re (z + 1) = 12-1), then prove that the locus of z is parabola.

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( operatorname{Re}(z+1)=|z-1| ) ( cot z=x+i y ) ( operatorname{se}(z+1)=x+1 ) ( therefore x+1=|(x-1)+i y| ) ( Rightarrow x^{2}+2 x+1=(x-1)^{2}+y^{2} ) ( -1+x^{2}+2 x+1=n^{2}-2 x+1+y^{2} ) ( Rightarrow quad y^{2}=4 x )

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