Frequency domain representation in discrete time signal and system

[@ironicallynormie3451]

thmx

[@korearunkumar]

Why should we take complex exponential as input?

[@AKHassan]

Because its is not affected at the output, meaning that output will always have the same complex exponential as the input. This is referred as eigenfunction. At the output you will get back your exact input (complex exponential / eigenfunction) plus some multiplicative term. e.g. consider differentiating or integrating a complex exponential. On the other hand, other functions would change.