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## Homework Statement

Prove that applying an infinitesimal rotation of angle k<<1 around the axis x

_{1}, then a boost of speed -k along the axis x

_{2}then the inverses of these is equal to a single boost of speed k^2 along the axis x

_{3}

## The Attempt at a Solution

Putting this into mathematical terms I get

e

^{-i*k*Jx1}*e

^{i*k*Gx2}*e

^{i*k*Jx1}*e

^{-i*k*Jx2}= e

^{-i*k2*Gx3}

However I don't really know where to go from here, the example we did in class only involved the rotations and we just used the matrix representations around the axis, but I don't know how exactly do it with the boosts.

Any help would be much appreciated.