UPSC NDA Math Model Paper 7

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.