Complex Variables · Number
Complex Numbers and Analytic Functions
Euler’s formula connects the exponential to rotation. Analytic functions satisfy the Cauchy-Riemann equations and are angle-preserving (conformal).
WHAT STUDENTS WILL LEARN
✓Represent complex numbers in rectangular, polar, and exponential form
✓Apply Euler’s formula: e^{iθ} = cosθ + i sinθ
✓Define complex functions as plane mappings
✓State the Cauchy-Riemann equations
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