$|r| = \sqrt{5}$, $\theta = \arctan(1/2)$; solution oscillates with exponentially growing amplitude $(\sqrt{5})^n$

$|r| = 2$, $\theta = \pi/4$; solution is purely real and grows like $2^n$

$|r| = 1$, $\theta = \pi/2$; solution is bounded and oscillates

Roots are undefined in polar form