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Is it possible in general to reduce number of variables of multi-variable real-to-real function by converting it to complex-to-real function, for example $g=f(a_1,a_2,a_3,a_4)$ in to $h=w(b_1,b_2)$? How to do it?

Update: Is it possible to two variable real-to-real function? How to obtain the formula?

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    In general no, if you want $w$ to be holomorphic. If that is not required, the trivial, and almost certainly utterly useless, way is to put $w(a_1+ia_2,a_3+ia_4)=f(a_1,a_2,a_3,a_4)$. – 2017-02-17
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    I tried solve trivial case, and resulted in functional equation. It is possible to solve it? Where can I read about this in more detail? – 2017-02-19
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    Sorry, I don't understand where a functional equation would come from. In any case, since as I indicated this is both trivial and useless, I highly doubt that anybody has written about it much, so there is no relevant literature for me to point to. – 2017-02-19

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