Prove that the complement of UTM's language is not turing recognizable.

Assume

L(UTM) is the language recognized by UTM , a language which constitute string set <M,w> where M is the description of a turing machine and w is any string.

Prove L'(UTM) - complement of L(UTM) is not turing recognizable.

Note:

I am looking for a proof which doesnt invoke the theorem that if L and L' are turing recognizable (recursively enumerable) L is turing decidable (recursive).

I am having this problem because...

I am thinking I can always construct a TM called NOT(universal turing machine) which simulates UTM and reverses the result. If such a turing machine exists is its language not L'(UTM)?

To find your mistake, if there is one, you would have to provide more details.

If your language L, written as sequences of {0,1}, is 1-L'==L'/.{0->1,1->0}, then L' is not necessarily the same thing as the complement of L. For instance, L=={{0,1},{1,0}} where they are the same.