In general, the zero state of a dynamical system of the form xt+1=Axt
x
t
+
1
=
A
x
t
is a stable equilibrium when all of the eigenvalues of A
A
are inside the unit circle in the complex plane. So if you have an eigenvalue of the form a+bi
a
+
b
i
, you get stability when a2+b2<1
a
2
+
b
2
<
1
. Since this is a homework question, I'll let you work out the rest of the problem from here. (This isn't going to be equivalent to solving −1−30k‾‾‾‾‾‾‾‾‾√<8
−
1
−
30
k
<
8
, though.)