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Singularities of f(z) are when [tex] (z^2 + 4), (z^2 + 1/4) = 0 [/tex]

In this case, the singularities are [tex] \pm2i , \pm\frac{i}{2} [/tex]

Lets call these singularities [itex] s [/itex] and [itex] s [/itex] is a simple pole if [itex] \lim_{z \to s} \frac{z}{(z^2 + 4) (z^2+1/4)} [/itex] exists.

I got all these singularities to be simple poles, correct or incorrect?