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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