### Instruction: Find all values of $z$ such that $z^4 - 4z^2 + 3 = 0$.  Enter all the solutions, separated by commas.### Response: I notice that this equation is a quadratic in $z^2$.
I can rewrite it as $(z^2 - 3)(z^2 - 1) = 0$.
Now, I can use the zero product property to find the values of $z^2$ that make the equation true.
Either $z^2 - 3 = 0$ or $z^2 - 1 = 0$.
Solving for $z^2$, I get $z^2 = 3$ or $z^2 = 1$.
To find the values of $z$, I need to take the square root of both sides.
Remembering that the square root can be positive or negative, I get $z = \pm \sqrt{3}$ or $z = \pm 1$.
So, there are four possible values of $z$ that satisfy the equation: $\sqrt{3}$, $-\sqrt{3}$, $1$, and $-1$.