#|z-(2+i)|<|z+1|#

by replacing #z# by #x+iy#,

#Rightarrow |x+iy-(2+i)|<|x+iy+1|#

by separating real parts and imaginary parts,

#Rightarrow |(x-2)+i(y-1)|<|(x+1)+iy|#

by find the norms,

#Rightarrow sqrt{(x-2)^2+(y-1)^2} < sqrt{(x+1)^2+y^2}#

by squaring,

#Rightarrow (x-2)^2+(y-1)^2<(x+1)^2+y^2#

by multiplying out,

#Rightarrow x^2-4x+4+y^2-2y+1 < x^2+2x+1 + y^2#

by cleaning up a bit,

#Rightarrow -2y < 6x-4#

by dividing by -2,

#Rightarrow y > -3x+2#

Hence, this is a region above the line #y=-3x+2#.

I hope that this was helpful.