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Applications of complex analysis?

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I am a math major and I really cannot understand complex analysis. I've tried it twice before doing so poorly on the midterms that I had to drop. I gave it a go during this summer and I again ended up dropping it.

I know that all the courses in the curriculum serve some purpose. I've taken differential equations and real analysis, so I can get my degree without ever taking complex analysis, but a lot of people have told me it's an integral part of a maths education, though they never specified why.

I want to know why. Why is complex analysis so important? What area outside of math (besides physics, electromagnetism; cannot stand physics) is complex analysis used?

Thank you


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