### 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 disguise, since I can rewrite it as $(z^2)^2 - 4(z^2) + 3 = 0$.
If I let $u = z^2$, then I have $u^2 - 4u + 3 = 0$, which is easier to solve.
I can factor this equation as $(u - 3)(u - 1) = 0$, so $u = 3$ or $u = 1$.
Now I need to find the values of $z$ that correspond to these values of $u$.
Since $u = z^2$, I can take the square root of both sides and get $z = \pm \sqrt{u}$.
Therefore, the solutions are $z = \pm \sqrt{3}$ and $z = \pm 1$.