Geodesic
Simultaneous approximations of real and complex numbers by algebraic numbers of special kind
Trudy Instituta matematiki, Tome 15 (2007) no. 1, pp. 3-9

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The paper is devoted to solving the problem about simultaneous approximation of real and complex number by special algebraic numbers. Here is given the proof of full analogue of Khintchine's theorem for convergence case. 
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     title = {Simultaneous approximations of real and complex numbers by algebraic numbers of special kind},
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N. V. Budarina; D. Dickinson; V. I. Bernik. Simultaneous approximations of real and complex numbers by algebraic numbers of special kind. Trudy Instituta matematiki, Tome 15 (2007) no. 1, pp. 3-9. http://geodesic.mathdoc.fr/item/TIMB_2007_15_1_a0/