# How do you force Mathematica to list all values of some multi-valued complex function at some point? [duplicate]

Let's say I have a complex-valued function $f(z) = \sqrt{z}$. When I plug $z = 1$ into it, it returns 1. I need it to return a list $\{-1,1\}$. Is it possible to force Mathematica to do that? I know it's possible to do that by solving $z^2 = 1$, but it involves finding inverse function to $\sqrt{z}$ first. And I don't want to do that.
• I vote to reopen this question as I feel, the linked answer doesn't really address the problem at the angle, at which this question (in my interpretation) approaches it. Many functions can be multivalued, depending on their definition. If the square root is defined as the number which, when squared, gives the original value, it does have two correct values. Consider, e.g. a function f[x_, y_] := x^(1/2) + y^(1/3). What I would like to get then, is a list of six values (two possible square roots combined with each of the three possible cubic roots). – LLlAMnYP Aug 11 '15 at 14:08
• @LLlAMnYP I think you've considerable expanded the expressed intent. (Why not ask and answer your own question?) I am confuzed by the OP's not wanting to solve $z^2 = 1$. If we're not allowed to use the algebraic equation defining the conjugates, I feel the problem has a very narrow scope, namely, just ±Sqrt. So the answer would simply be f[z_] := {-1, 1} Sqrt[z]. If that is not the answer, then the Q is unclear. – Michael E2 Aug 11 '15 at 16:33