Singularities and integrating

Hi, I have some past papers with no answers and not much idea on how to find them, any help appreciated!!

For part a) is it something about$\displaystyle z^4$ lies on the circle with radius $\displaystyle R^4 $and so its minimal distance to -sqrt(2)a i$\displaystyle s R^2-4a^4$?

part b) use the M-L lemma to show int(f)$\displaystyle <$$\displaystyle \Pi R z e^iz$/$\displaystyle R^4-4a^4$ which tends to zero as $\displaystyle R$ tends to infinity?

c) singularities would be $\displaystyle z^4=-4a^4 $though not sure what these are . Think I may have to brake $\displaystyle z^4+4a^4$down into composite parts e.g.$\displaystyle (z^2-2ia^2)(z^2+2ia^2)$

part d) I have no idea!

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