# complexideas

Algebra Level 2

If $$x+\dfrac 1x = \sqrt{58}i$$, then it can be proven that $$\sin (x^2) + \sin \left(\dfrac 1{x^2}\right) + \cos (m) = 0$$, where $$m$$ is a positive integer. Find the value of $$\cos(m+2)$$.



Notation: $$i = \sqrt{-1}$$ denotes the imaginary unit.

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