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## Homework Statement

Prove that the magnitude of the general four velocity U = (γc, γv

_{x}, γv

_{y}, γv

_{z}) is always equal to c.

## The Attempt at a Solution

|U| =

=[itex]\sqrt{(\gamma c)^{2}+(\gamma v_{x})^{2}+(\gamma v_{y})^{2}+(\gamma v_{z})^{2}}[/itex]

=[itex]\gamma\sqrt{c^{2}+v_{x}^{2}+v_{y}^{2}+v_{z}^{2}}[/itex]

=[itex]\gamma\sqrt{c^{2}+v^{2}}[/itex]

=[itex]c\gamma\sqrt{1+\frac{v^{2}}{c^{2}}}[/itex]

=[itex]c\frac{\sqrt{1+\frac{v^{2}}{c^{2}}}}{\sqrt{1-\frac{v^{2}}{c^{2}}}}[/itex]

As you can see, somehow I'm off by a minus :\ Can someone help me out here? I'm guessing these two square roots are supposed to cancel somehow.

Any help is appreciated :\ Been staring at this for a while now