The greatest and the least absolute value of z+1 ,where |z+4|≤3 are respectively

Given that |z+1|=|z+4−3|....................(i) |z+4−3|≤|z+4|+|−3|≤3+3=6 [given |z+4|≤3 &|−3|=3 ]∴|z+1|≤6 Again |z+1|≥0 [modules is always non-negative]∴ least value of |z+1| may be zero ,which occurs when z =–1,for  z=–1⇒|z+4|=|−1+4|=3 which satisfies the given condition that |z+4|≥3 hence, the least and the greatest  values of |z+1|  are 0 and 6