z = r (cosθ + isinθ) x + by + cz + d = 0 (f(−x) = f(x), ∀ x ∈ D) −x + 2y + z + t = −1 2x + 2y + z + 4t = 0 C = {z = x + iy x, y ∈ IR} z = −1 + i (f(−x) = f(x), ∀ x ∈ D)

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z = −1 + i nα = θ + 2πk u = ρ (cosα + isinα) f(x) = 3x − 2 z = r (cosθ + isinθ) ax + by + cz + d = 0 a (f(x + T) = f(x), ∀ x ∈ IR) (f(−x) = f(x), ∀ x ∈ D) 2x + 2y + z + 4t = 0 [x0 −r, x0 + r] (cosnα + isinnα) = (cosα + isinα)n z = −1 + i nα = θ + 2πk u = ρ (cosα + isinα)

The solution for a utility market operator