I have this problem with a complex integral and I'm having a lot of difficulty solving it:(adsbygoogle = window.adsbygoogle || []).push({});

Show that for R and U both greater than 2a, \exists C > 0, independent of R,U,k and a, such that $$\int_{L_{-R,U}\cup L_{R,U}} \lvert f(z)\rvert\,\lvert dz\rvert \leqslant \frac{C}{kR}.$$

Where a > 0, k > 0, $$L_{-R,U} = \{-R + iy \mid 0 \leqslant y \leqslant U\}$$, $$L_{R,U} = \{ R + iy \mid 0 \leqslant y \leqslant U\}$$ and $$f(z) := \frac{z e^{ikz}}{z^2+a^2}$$

I don't really know where to start, or what to use. Any help would be greatly appreciated, thanks

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# I Complex integral problem

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