Complex Practice Exam 1
This practice exam contains sample questions. The actual exam will have
fewer questions, and may contain questions not listed here.
1. Be prepared to explain the following concepts, definitions, or theorems:
• A complex number, polar coordinates, rectangular coordinates
• Add, Multiply, Sub, Div, Conjugate, abs Value, graphical interpretations
of these
• Complex roots
• Mapping properties of complex functions
• Arg(z) and arg(z)
• The limit of a complex function f(z) as z approaches c is L
• Continuity of a complex function f(z) at a point z = c
• The complex derivative of a function f(z)
• Analytic function and Entire function
• CR equations
• f(z) analytic & f’(z) = 0, f(z) analytic & f-conjugate analytic, f(z) analytic
and |f(z)| constant
• Harmonic function and harmonic conjugate of a function u (incl. how to
find)
• , sin(z), cos(z), log(z), and Log(z)
• Euler’s Formula, De Moivre’s Formula
• Complex parametric functions z(t), their integrals and derivatives
• Different paths (line segments and circles)
• Contour Integrals
2. Describe the set of points z such that
(a)
(b)
(c)
3. Let . Draw, in one coordinate system, , , , and
