Complex Analysis - 4 Video Lecture | CSIR NET Crash Course for Physical Science - CSIR NET Physical Science

FAQs on Complex Analysis - 4 Video Lecture - CSIR NET Crash Course for Physical Science - CSIR NET Physical Science

1. What are the basic properties of complex numbers?
Ans. Complex numbers consist of a real part and an imaginary part, denoted as a + bi, where 'a' is the real part, 'b' is the imaginary part, and 'i' is the imaginary unit. They follow the properties of addition, subtraction, multiplication, and division.
2. How is a complex function defined in complex analysis?
Ans. In complex analysis, a complex function is a function that maps complex numbers to complex numbers. It can be expressed as f(z) = u(x, y) + iv(x, y), where z = x + iy, u and v are real-valued functions of x and y, and i is the imaginary unit.
3. What is the Cauchy-Riemann equation in the context of complex analysis?
Ans. The Cauchy-Riemann equation is a set of partial differential equations that must be satisfied by a complex function to be considered analytic. It relates the partial derivatives of the real and imaginary parts of a complex function with respect to x and y.
4. How is contour integration used in complex analysis?
Ans. Contour integration is a powerful technique in complex analysis that involves integrating complex functions along a curve in the complex plane. It is used to evaluate complex integrals, calculate residues, and solve differential equations.
5. What are some applications of complex analysis in physics?
Ans. Complex analysis is widely used in physics for various applications, such as solving differential equations in quantum mechanics, analyzing fluid flow in aerodynamics, and studying electromagnetic fields in electromagnetism.

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