Imaginaringly fun problem

Algebra Level pending

Let \(w= \frac { z }{ { z }^{ 2 }+1 } \)

If \(z=x+iy\), where \(i=\sqrt { -1 }\) and \(y\neq 0\) , \({ z }^{ 2 }+1 \neq 0\)

And it is known that \(Im(w)=0\)

What is the value of \(\left| z \right|\) ?

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