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I'm currently solving some university E&M homework problems and to solve input impedance, we were given this formula (from Fundamentals of Applied Electromagnetics 6th Ed):

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But when I browse online on the subject matter, the presented formulas are overwhelmingly as follows: enter image description here

I'm totally stumped on the difference between these two, I read through both derivations and don't understand how they arrive to this conclusion. Any help will be greatly appreciated!

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