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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
3 months, 2 weeks ago

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