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Complex Analysis Shortcuts & Key Formulas Prepared by Annu Sheoran, Study notes of Mathematics

Chaudhary Ranbir Singh UniversityMathematics

This concise reference guide covers the essential formulas and tricks from Complex Analysis, tailored specifically for quick revision. It includes step-by-step handwritten notes on Cauchy-Riemann equations, Euler’s formula, polar forms, residue theorem, and contour integration — all arranged in a logical academic flow for maximum clarity. Perfect for exam prep and competitive exams.

Typology: Study notes

2024/2025

Available from 04/16/2025

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J f(2)dz Ig Shorteut Techniques in Complex Analysis - Exam Hacks! fre dz Ca Prepared by: Annu Sheoran For Z Mathematics Students Title: Shortcut Techniques in Complex Analysis — Exam Hacks! 1. Cauchy-Riemann Equations Trick ¢ To check analyticity of f(z) = u(x, y) + iv(a, y), quickly use: Ou Ov Ou Ov dx Oy Oy Oa e Shortcut: If partial derivatives are hard, try writing in terms of z = x + zy directly if possible. 4. Polar Form Quick Conversion e Any complex number z = re’? where: r=|z)\=V2e+y’, O0=tan '(y/x e Shortcut: This is very handy for multiplication and division of complex numbers. 5. Fast Contour Integration Tip e For circular paths: If is a circle around 0 and f(z) = [soe = 0 ifnAél 231 ifin=1 i PAL