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I need help simplifying the following:

|[itex]\sqrt{z^2 -1}[/itex] +z| + |[itex]\sqrt{z^2 -1}[/itex] -z|

What I did was I rewrote z in polar coordinates, but I ran into some difficulties taking the square root of [itex]r^2(cos2θ-sin2θ)-1[/itex].

I also tried rewritting z in exponential form, but also had problems. Help?