Re[ArcTan[x, y]] == ArcTan[(Cos[(1/2) ArcTan[-Im[x]^2 - Im[y]^2 + Re[x]^2 + Re[y]^2, 2 Im[x] Re[x] + 2 Im[y] Re[y]]] (-Im[y] + Re[x]))/ ((2 Im[x] Re[x] + 2 Im[y] Re[y])^2 + (-Im[x]^2 - Im[y]^2 + Re[x]^2 + Re[y]^2)^2)^(1/4) + ((Im[x] + Re[y]) Sin[(1/2) ArcTan[-Im[x]^2 - Im[y]^2 + Re[x]^2 + Re[y]^2, 2 Im[x] Re[x] + 2 Im[y] Re[y]]])/ ((2 Im[x] Re[x] + 2 Im[y] Re[y])^2 + (-Im[x]^2 - Im[y]^2 + Re[x]^2 + Re[y]^2)^2)^(1/4), (Cos[(1/2) ArcTan[-Im[x]^2 - Im[y]^2 + Re[x]^2 + Re[y]^2, 2 Im[x] Re[x] + 2 Im[y] Re[y]]] (Im[x] + Re[y]))/ ((2 Im[x] Re[x] + 2 Im[y] Re[y])^2 + (-Im[x]^2 - Im[y]^2 + Re[x]^2 + Re[y]^2)^2)^(1/4) - ((-Im[y] + Re[x]) Sin[(1/2) ArcTan[-Im[x]^2 - Im[y]^2 + Re[x]^2 + Re[y]^2, 2 Im[x] Re[x] + 2 Im[y] Re[y]]])/ ((2 Im[x] Re[x] + 2 Im[y] Re[y])^2 + (-Im[x]^2 - Im[y]^2 + Re[x]^2 + Re[y]^2)^2)^(1/4)]

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2001-10-29