Given the reverse triangle inequality, mod(a+b+c) is greater than or equal to mod(a)- mod(b) - mod(c).
Suppose a, b, c are complex numbers such that mod(a)=4, mod(b)=10 and mod(c)=1. What is the smallest possible value that mod(a+b+c) can attain? Justify your answer.
I know the answer is 5, and that it relates to b's dominance over the over numbers but am struggling to explain how this is the case?
Could someone please shine some light on this for me please?