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neginf
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How are complex numbers used in physics ?
Do they have any physical meaning ?
Do they have any physical meaning ?
neginf said:Are there any physical quantities that are complex ?
Do physical quantities need to be ordered ?
The square root of a negative number is a negative number when squared and a positive number when cubed.
I'm guessing it's just a typo, but i³ = -i = 1/i. You need 4th power to get positive.LostConjugate said:The square root of a negative number is a negative number when squared and a positive number when cubed. This is convenient as it has the properties of being oscillatory.
Studiot said:Excuse me?
Are you asserting the i is negative, since i x i x i = -i ?
neginf said:How are complex numbers used in physics ?
Do they have any physical meaning ?
Now you're making mistakes. Imaginary unit to even power is real, but it can be positive or negative.
Studiot said:Whilst i raised to any even power is definitely positive, i itself is neither positive nor negative.
Complex numbers are numbers that contain a real part and an imaginary part, usually represented as a + bi. They are used in physics to represent quantities that have both magnitude and direction, such as electric and magnetic fields.
In quantum mechanics, complex numbers are used to describe the state of a quantum system. The wave function of a particle is a complex-valued function, and the Schrödinger equation, which describes the evolution of a quantum system, involves complex numbers.
Complex numbers provide a mathematical framework to solve physical problems that involve quantities with both real and imaginary components. They allow for more precise and accurate calculations in various areas of physics, such as electromagnetism and quantum mechanics.
Yes, complex numbers are used in many other branches of physics, such as fluid dynamics, signal processing, and optics. They are also used in engineering and other fields that deal with complex systems and phenomena.
Yes, complex numbers can have physical interpretations in certain situations. For example, in quantum mechanics, the imaginary part of a wave function has a physical significance representing the phase of a particle. In electromagnetism, the real and imaginary components of a complex number can represent the electric and magnetic fields, respectively.