Are we only allowed to do line integrals on a complex plane?(Is the line integral the only type of integral on the complex plane?) Do we have something like surface integral on a complex plane? If the answer is no, why we cannot do that?
2026-04-12 09:32:50.1775986370
A conceptual question on complex plane: Can we do any other type of integration on a complex plane?
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In mathematics you are "allowed" to do anything that's logically consistent. Which allowed things you choose to focus on depends on what you are studying.
Line integrals are central to the study of complex analysis, so that's what you see there.
You can also do an ordinary double integral of a complex valued function over a region in the plane if you find that the need comes up.