### Instruction: Find all values of $z$ such that $z^4 - 4z^2 + 3 = 0$.  Enter all the solutions, separated by commas.### Response: To solve this equation, I notice that it is a quadratic equation in disguise, if I let $y = z^2$.
Then I can rewrite the equation as $y^2 - 4y + 3 = 0$, which is easier to factor.
I get $(y - 1)(y - 3) = 0$, so $y = 1$ or $y = 3$.
But I want to find $z$, not $y$, so I need to undo the substitution and take the square root of both sides.
If $y = 1$, then $z^2 = 1$, so $z = \pm 1$.
If $y = 3$, then $z^2 = 3$, so $z = \pm \sqrt{3}$.
Therefore, the solutions are $z = 1, -1, \sqrt{3}, -\sqrt{3}$.