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(cosθ+isinθ), then we have
|r2(cos2θ+isin2θ)−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
r2<2cos(2θ)
The set is inside the curve defined by its polar equation
r=√2cos(2θ)
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