### Instruction: Find all values of $z$ such that $z^4 - 4z^2 + 3 = 0$.  Enter all the solutions, separated by commas.### Response: To find the values of $z$ that satisfy this equation, I will try to factor the left-hand side into two simpler expressions.
I notice that the equation has the form $a^2 - 4a + 3 = 0$, where $a = z^2$.
I know that $a^2 - 4a + 3$ can be factored as $(a-1)(a-3)$, so I can rewrite the equation as $(z^2-1)(z^2-3) = 0$.
Now, I can use the zero product property to say that either $z^2-1 = 0$ or $z^2-3 = 0$.
Solving for $z^2$, I get $z^2 = 1$ or $z^2 = 3$.
Taking the square root of both sides, I get $z = \pm 1$ or $z = \pm \sqrt{3}$.
Therefore, there are four possible values of $z$ that make the equation true.