Problem:
If is the set of points in the complex plane such that is a real number, then is a
Answer Choices:
A. right triangle
B. circle
C. hyperbola
D. line
E. parabola
Solution:
The set consists of all complex numbers of the form
for some real number . Since consists of all real multiples of , each point in is on the line through the origin and , and conversely.
Let . Then , which is real if and only if , the equation of a line.