# How to compute with roots of negative numbers

I have heard that taking roots of negative numbers gives me multiple values, like $\sqrt{-1}=\pm i$. But how can I compute expressions that takes multiple times of numbers having several values? Like is $\sqrt{-1}+\sqrt{-1}=\pm i+\pm i=-2i,0,2i$? I think that in third degree polynomial equations one has to compute sum of two multivalued roots.

• What you have "heard" is not quite accurate. In short, $i$ is the imaginary unit with the property $i^2=-1$ When working with complex numbers, it is better to avoid notations as $\sqrt{-1}$ As a consequence, that arithmetic operation you did with those two radicals is something one should frown upon (to express my concern rather diplomatic...) Here is a nice link for self learning: math.stackexchange.com/questions/144364/… – imranfat Mar 6 '16 at 18:43