Find the first three iterates of the function f(z) = z2 + c with a value of c = 1 + 2i and an initial value of z0 = 0.

Starting with z₀ = 0, the first iterate is z₁ = 0² + (1 + 2i) = 1 + 2i. Then z₂ = (1 + 2i)² + (1 + 2i) = -2 + 6i, and z₃ = (-2 + 6i)² + (1 + 2i) = -31 - 22i. These iterates match choice C.

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