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This article has been edited from the text of a talk given at the BSHM Research in Progress meeting, held at The Queen's College, Oxford, in March 2012. The ‘Tait–Maxwell school-book’ (which is preserved by Edinburgh's Maxwell Foundation) was intended as a fair-copy book in which Tait and Maxwell (principally Tait) could preserve propositions, theorems and worked-through examples while at the Edinburgh Academy. My transcription of the school-book includes Tait's notes on a lecture he had heard on the geometrical representation of complex numbers. The lecture, delivered by no less than the Right Revd Bishop of Edinburgh, surely constitutes Tait's first introduction to complex numbers and as such merits discussion along with associated historical insights. [ABSTRACT FROM PUBLISHER]