If $\|a-b\| < \|b\|$ what follows for $\|a\|$?

Question

Let $$ \|a-b\| < \|b\| $$ where $a, b \in C^n$. Аre they following any relations for $\|a\|$ or $\|b\|$?

($\|.\|$ is the 2-norm of vectors)

Answer 1

That says geometrically that $a$ is inside the ball of radius $\|b\|$ with center $b$ .

Answer 2

It follows that $a$ cannot be the null vector and that therefore $\lVert a\rVert\neq0$. And it also follows that$$\lVert a\rVert=\lVert a-b+b\rVert\leqslant\lVert a-b\rVert+\lVert b\rVert<2\lVert b\rVert.$$