Hi.

I'm presenting you how You derive Complex version of famous Green's Theorem as an exercise using Real Green's Theorem.

It is very aesthetic. You don't work on region and its boundary (only You know boundary is partially C1). Function does not have to be differentiable in COMPLEX sense! (If it is, then both integrals are equal 0 - everyone who passed one introductory course in one variable complex analysis knows why).

So, even if You don't understand what is written here, I encourage You to learn Math with MESScience, he does very good videos. One day You will understand what I put here. Maybe these beautiful writings will inspire You.

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http://gestyy.com/eqs9w4

http://gestyy.com/eqs9rs