I am looking for all the solutions of $x^4+2tx^2+1=0$   

Is there any "quick" way to figure out all the complex-solutions $\pi\_i(t)$ where $i=1,...4$ ? 

I got $\pi\_1(t)=\sqrt{-t+\sqrt{t^2-1}}\sqrt{t-\sqrt{t^2-1}}\sqrt{-t+\sqrt{1-t^2}}$   

 but apparently I am too "stupid" to verify my calculation. I always end up making mistakes (hopefully) in my calculation.

Would appreciate any help