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+36 Therefore, maximum possible value for ∣z+1∣ is 6.