complex analysis - Describe the set whose points satisfy the following relation: $|z^2 - 1| < 1$

There is a hint which states to use polar coordinates, but I feel like that complicates the problem more. As far as trying it myself, I get lost very early on. If we take $z = r(\cos{\theta} + i\sin{\theta})$, then we have

$|r^2(\cos{2\theta} + i\sin{2\theta}) - 1| < 1$

But I have no idea how to find the modulus of this point with that extra $-1$ in there.

Answer

Hint

Taking the square, we get after simplifying

$r^2<2\cos(2\theta)$

The set is inside the curve defined by its polar equation

$r=\sqrt{2\cos(2\theta)}$