Simplifying Complicated Expression: ((i+1)^{n+1} - (i-1)^{n+1})

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Poopsilon
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I've got this complicated expression that I'm trying to simplify and this is one piece which I feel might have a really simple form: [itex]((i+1)^{n+1} - (i-1)^{n+1))[/itex] for n ≥ 0. Thanks.
 
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can you describe it a little more? is this for homework?

Does the i mean sqrt(-1)? If so then isn't the i-1 related to the complex conjugate of i+1?