Parameter range from complex inequality

[DanMat]

Homework Statement

Hi Guys,
I try to find the range for parameters phi1 and phi2 were the autoregressive process below is stationary.
We have the process X(t)+phi1*X(t-1)+phi2X(t-2)=Epsilon(t) (1)

Homework Equations

We get the characteristic polynomial F(z)=z^2+phi1*z+phi2 (2)
The process is stationary if the roots z are within the unit circle.

The Attempt at a Solution

I can off course easily find the roots of the polynom:
z1=-phi1/2+sqrt(phi1^2/4-phi2) (3)
z2=-phi1/2-sqrt(phi1^2/4-phi2) (4)

Now we need to find the range for phi1 and phi2, such that the absolute value of z1 and z2 is <1. Since the phi's can be complex, this is a bit tricky and I'm stuck here. I tried substituting phi1=a+bi and phi2=c+di but I can't get rid of the squareroot on the RHS of (3) and (4). Any good ideas, how to solve this?

 

[DanMat]

Solved it. It's not the phi's that can get complex, only the roots. Then it's "easily" possible to find the allowed parameter range.