We will look for the Green's function for R2In particular, we need to find a corrector function hx for each x 2 R2 , such that ∆yhx(y) = 0 y 2 R2 hx(y) = Φ(y ¡x) y 2 @R2 Fix x 2 R2We know ∆yΦ(y ¡ x) = 0 for all y 6= xTherefore, if we choose z =2 Ω, then ∆yΦ(y ¡ z) = 0 for all y 2 Ω Now, if we choose z = z(x) appropriately, z =2 Ω, such that Φ(y ¡ z) = Φ(y ¡ x) for y 2Letting f R !C by f(x) = cosx isinx, (22) is the same as f(x y) = f(x)f(y) That is, if you calculate the real and imaginary parts of f(x y) and of f(x)f(y), then equality of the real parts is the addition formula for cosine and equality of the imaginary parts is the addition formula for sineNanotechnology 19, (08) 1 Densitycontrolled growth of aligned ZnO nanowire arrays by seedless chemical approach on smooth surfaces pdf S Xu, CS Lao, B Weintraub, ZL Wang Journal of Materials Research 23, 7277 (08) Readers may view, download, store, and print these research protocols and results for temporary copying Suai R Gwynt You...