When it comes to integration of some function f(t) where t is real, I would just treat everything as a constant and integrate it.(adsbygoogle = window.adsbygoogle || []).push({});

Even with complex functions f(t) = u(t) + iv(t) why can't I just treat i as a constant and just integrate?

Here is an example:

[tex]\int_{0}^{\pi/2}e^{t+it}dt[/tex]

What's wrong with imaginary i being an ordinary constant giving you an easy answer of:

[tex](1+i)e^{\frac{\pi}{2}(1+i)} - (1+i)[/tex]

Whereas treating the function as two seperate quantities, "real" and "imag" would require integration by parts giving a different answer (I know there is a simpler integration method but that's beside the point).

My main question is what is the physical interpretation of the two methods? I was never taught complex integration so I don't know.

Thanks guys.

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# A physical meaning to complex integration

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