# Complex Generalisation of Infinite Tetration

Algebra Level 4

Tetration is defined as

$\large {^{n}a} = \underbrace{a^{a^{\cdot^{\cdot^{a}}}}}_n$

If $$z$$ is a complex number, then find the value of

${^{\infty}z}$

Details and Assumptions:

$$W$$ is the Lambert's W function. It is defined as" $$x = W(x) e^{W(x)}$$ for all complex number $$x$$.

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