ILL 1990 Problem 67

Let $a + bi$ and $c + di$ be two roots of the equation $x^n = 1990$ , where $n \geq 3$ is an integer and $a,b,c,d \in \mathbb R$ . Under the linear transformation $f =\left(\begin{array}{cc}a&cb &d\end{array}\right)$ , we have $(2, 1) \to (1, 2)$ . Denote $r$ to be the distance from the image of $(2, 2)$ to the origin. Find the range of $r.$