Express |z + 1| in terms of |z + 4| as follows: |z+1|=|z+4+(−3)| It is given that |z+4|3 . Use the above condition along with triangle inequality as follows: |z+1|=|z+4+(−3)| |z+4|+|(−3)| ...Using triangle inequality 3+3 6 Therefore, maximum possible value for |z+1| is 6.