At Jena, Frege attended lectures by Ernst Karl Abbe, who subsequently became Frege’s mentor and who had a significant intellectual and personal influence on Frege’s life.  Frege transferred to the University of Göttingen in 1871, and two years later, in 1873, was awarded a Ph.D. in mathematics, having written a dissertation under Ernst Schering titled Über eine geometrische Darstellung der imaginären Gebilde in der Ebene (“On a Geometrical Representation of Imaginary Forms in the Plane”). Frege explains the project in his thesis as follows: “By a geometrical representation of imaginary forms in the plane we understand accordingly a kind of correlation in virtue of which every real or imaginary element of the plane has a real, intuitive element corresponding to it” (Frege 1873, translation in McGuinness (ed.)  1984, 3).  Here, by ‘imaginary forms’, Frege is referring to imaginary points, imaginary curves and lines, etc.  Interestingly, one section of the thesis concerns the representation of complex numbers by magnitudes of angles in the plane.