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# What is the geometric significance of integration in the complex plane?

In BC Calc we learned something called "complex integration" where if we were integrating something like $$\displaystyle \int e^x \cos x \, dx$$, we could rewrite as $$\mathfrak{Re} \left( \displaystyle \int e^x e^{ix} \, dx \right)$$. What does it mean geometrically when we integrate with complex numbers and then take the real part?

Note by Hobart Pao
1 year ago