# Literally complex functions

Algebra Level 3

Four functions are defined as follows:

$$f(x) = x(x+1)$$

$$g(x) = x^2+3$$

$$h(x) = g(x) \cdot g^2(x)$$

$$h'(x) = g(x) + g^2(x)$$

Find the value of $$k$$ given that $$kf^2(2) = h(i) \cdot h'(i)$$ where $$i$$ denotes the imaginary unit.

Note: $$f^n(x) = f^{n-1} f(x)$$

$$f^n(x)$$ is NOT $$(f(x))^n$$

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