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I cannot work out how the working shown in the attached pic is well, er worked out!

Could someone explain the ins and outs of the complex analysis of taking the real or imaginary parts of some formula, for example in the context of the my case.

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Quantum Mechanics algebra - complex analysis

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