So we know that [Hodge duality](http://en.wikipedia.org/wiki/Hodge_dual) works this way(adsbygoogle = window.adsbygoogle || []).push({});

$$⋆(dx^i_1 \wedge ... \wedge dx^i_p)= \frac{1}{(n-p)!} \epsilon^{i_1..i_p}_{i_{p+1}..i_n} dx^{i_{p+1} } \wedge dx^{i_n}$$

where p represents the p in p-form and n is the dimensional number.

My question is: How does hodge duality work on the imaginary number "i" on one hand and on partial derivative like $$\partial_x\alpha$$ let us say on the other where $$\alpha$$ is a complex function.

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# Hodge duality and some properties

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