EEE 402: Complex Analysis for Electrical Engineers First Semester Examination

Complex analysis paper for the electrical and electronic engineering degree, sat on Wednesday the thirteenth of March from eight until ten. Question one is compulsory at thirty marks: the definitions of a conformal mapping and of an analytic function, the Laurent series expansion of a reciprocal cubic about a point with the residue read off it, the image of a circle under the reciprocal mapping, a contour integral round a given centre evaluated with the integral formula, a line integral along a parabola between two points, the Z-transform of a power sequence, and the real part that makes a given imaginary part analytic with the function expressed in terms of z. The optional questions test the continuity of a function defined piecewise at a point, the principal value of the logarithm of one minus i, the expansion of the cosine of a complex argument, the singular points of a rational function, the necessary condition for a function to be analytic in a domain proved from the Cauchy-Riemann equations, residues at singular points used to evaluate an integral round a circle, an integral evaluated with Cauchy's theorem, the value of an expression in two given complex numbers, all the values of a complex number raised to an imaginary power with its principal value, and an integral evaluated with the Cauchy integral formula.