On Conjugate Functions, or Algebraic Couples

By William R. Hamilton

William R. Hamilton gave a report On conjugate functions, or algebraic couples, as tending to illustrate generally the doctrine of imaginary quantities, and as confirming the results of Mr Graves respecting the existence of two independent integers in the complete expression of an imaginary logarithm at the meeting of the British Association for the Advancement of Science, held at Edinburgh in 1834. In this report Hamilton describes how the theory of complex numbers can be developed as a theory of algebraic couples (i.e., ordered pairs of real numbers).

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D.R. Wilkins
School of Mathematics
Trinity College, Dublin