Elliptical phase-plane trajectories occur in a 2 x 2 DE system with purely imaginary eigenvalues, which happens when Tr A = 0 and |A| > 0. Thus, for

(a) Show that

is an eigenvector for

(b)

Multjplying the vector in (a) by the complex scalar 1 / b(a + βi) gives a new vector

Show that is also an eigenvector for

(c) Explain how writing

gives real and imaginary parts,  and for the com-plex eigenvector that re completely different from the real and imaginary parts

=|a bland -IAI - a- 4