### Instruction: Find all values of $z$ such that $z^4 - 4z^2 + 3 = 0$.  Enter all the solutions, separated by commas.### Response: I recognize this equation as a quadratic equation in disguise, since $z^4$ is the square of $z^2$.
To make it more clear, I can let $u = z^2$, and then the equation becomes $u^2 - 4u + 3 = 0$.
Now I can factor this equation as $(u - 3)(u - 1) = 0$, which means that $u = 3$ or $u = 1$.
But I want to find $z$, not $u$, so I need to take the square roots of both sides of these equations.
For $u = 3$, I get $z^2 = 3$, which means that $z = \pm \sqrt{3}$.
For $u = 1$, I get $z^2 = 1$, which means that $z = \pm 1$.
Therefore, the four solutions for $z$ are $1, -1, \sqrt{3}, -\sqrt{3}$.