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## Main Question or Discussion Point

I've been trying to work through this and see whether you can take an "area" in the complex plane, have x,y vary in some interval, and integrate complex functions over that "area."

The math doesn't seem to work out; plus intuitively, if you're gonna sum up a function in a complex variable z, you better be able to say "I will sum up z from some z_a to z_b varied by a parameter t," but if we're looking at an "area" in the complex plane, we cannot say exactly what z varies from, only what it's components x,y vary.

I even tried two parameters in the plane and that didn't seem to yield. Is the reason because the complex plane is actually at 2D depiction of the 1-dimensional vector space C^1?? Therefore, the idea of a double integral over two parameters makes no sense?

Thanks guys

The math doesn't seem to work out; plus intuitively, if you're gonna sum up a function in a complex variable z, you better be able to say "I will sum up z from some z_a to z_b varied by a parameter t," but if we're looking at an "area" in the complex plane, we cannot say exactly what z varies from, only what it's components x,y vary.

I even tried two parameters in the plane and that didn't seem to yield. Is the reason because the complex plane is actually at 2D depiction of the 1-dimensional vector space C^1?? Therefore, the idea of a double integral over two parameters makes no sense?

Thanks guys