Answer:
[tex]x=i[/tex]
(i.e., [tex]x[/tex] is a complex number)
Step-by-step explanation:
We have
[tex]wx^2+w=w(x^2+1)=0[/tex]
Then it must be that
[tex]x^2+1=0[/tex]
as we are told [tex]w[/tex] is a positive integer (i.e., [tex]w\neq 0[/tex]), then it follows that
[tex]x^2=-1[/tex]
which is the definition of the unit imaginary number ([tex]i^2=-1[/tex]), so we may conclude:
[tex]x=i[/tex]
