We describe the computation of the amplitude A_2 for a kaon to decay into two pions with isospin I=2. The results presented in the letter Phys.Rev.Lett. 108 (2012) 141601 from an analysis of 63 gluon configurations are updated to 146 configurations giving Re$A_2=1.381(46)_{textrm{stat}}(258)_{textrm{syst}} 10^{-8}$ GeV and Im$A_2=-6.54(46)_{textrm{stat}}(120)_{textrm{syst}}10^{-13}$ GeV. Re$A_2$ is in good agreement with the experimental result, whereas the value of Im$A_2$ was hitherto unknown. We are also working towards a direct computation of the $Kto(pipi)_{I=0}$ amplitude $A_0$ but, within the standard model, our result for Im$A_2$ can be combined with the experimental results for Re$A_0$, Re$A_2$ and $epsilon^prime/epsilon$ to give Im$A_0/$Re$A_0= -1.61(28)times 10^{-4}$ . Our result for Im,$A_2$ implies that the electroweak penguin (EWP) contribution to $epsilon^prime/epsilon$ is Re$(epsilon^prime/epsilon)_{mathrm{EWP}} = -(6.25 pm 0.44_{textrm{stat}} pm 1.19_{textrm{syst}}) times 10^{-4}$.
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