Is there any complex value for $x$ where $|x| < 0$?

Question

What I'm really asking is if I get to a point in a calculation where I have $|x| = -4$, do I say

There is no solution for $x$

or do I say

There is no solution for $x ∈ ℝ$

Answer 1

Well, first of all, if it depends on where you are looking for the solution. It is true that there is no solution for $x\in\mathbb C$, but if the question starts with "Does there exist such $x\in\mathbb N$[...]", then I would still say "there is no solution in $\mathbb N$".

Answer 2

if $$x=a+ib$$ then we get $$|x|=\sqrt{(a^2+b^2)}$$ and this is not negative