Question

( 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 )

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

Solution