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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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Dec 27, 2024 Last updated |
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