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koolraj09
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Hi guys.
What is really the need for complex numbers? Is there any physical meaning associated with it?
What is really the need for complex numbers? Is there any physical meaning associated with it?
koolraj09 said:Hi guys.
What is really the need for complex numbers? Is there any physical meaning associated with it?
Pythagorean said:I always thought i was a geometric transform operator for two-dimensional systems. I'm still not quite sure what the difference between A 2D vector and complex number is, especially if the vectors are normalized so that their inner product is 1.
noone123 said:I'm still doing school maths, but I can see how complex numbers can be used to represent force vectors if you know what I mean. So I guess it really useful in physics
Complex numbers are numbers that consist of a real part and an imaginary part. They are written in the form a + bi, where a and b are real numbers and i is the imaginary unit, which is defined as the square root of -1.
Complex numbers have a variety of applications in physics, such as in electrical engineering, quantum mechanics, and signal processing. They are used to represent quantities that have both magnitude and direction, such as electrical current and wave amplitudes.
Yes, complex numbers can have a physical interpretation. The real part of a complex number represents the physical quantity, while the imaginary part represents the phase or direction of the quantity. For example, in alternating current circuits, the real part of a complex number represents the voltage, while the imaginary part represents the phase difference between the voltage and current.
No, complex numbers are not typically used in classical mechanics. Classical mechanics deals with physical systems that can be described using real numbers. However, complex numbers are commonly used in quantum mechanics, which deals with the behavior of particles at a microscopic level.
The geometric interpretation of complex numbers is that they can be represented as points on the complex plane, with the real part representing the x-axis and the imaginary part representing the y-axis. The magnitude of the complex number represents the distance from the origin, and the angle from the positive real axis represents the phase or direction.