Geodesic
Functional Dependence and Analytic Functions
Canadian mathematical bulletin, Tome 22 (1979) no. 3, pp. 367-369

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DOI

Without appealing to the Cauchy theorem or its corollaries, it is proved that the real and imaginary parts of a non-constant complex-valued analytic function of several complex variables are functionally independent. This unifies and generalizes some results sporadically treated in standard treatises on function theory. 
Ramankutty, P. Functional Dependence and Analytic Functions. Canadian mathematical bulletin, Tome 22 (1979) no. 3, pp. 367-369. doi: 10.4153/CMB-1979-047-7
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     title = {Functional {Dependence} and {Analytic} {Functions}},
     journal = {Canadian mathematical bulletin},
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     year = {1979},
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     number = {3},
     doi = {10.4153/CMB-1979-047-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1979-047-7/}
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