using contraction and expansion
electrical engineers and quantum mechanics use them.
Complex numbers are theoretically interesting; they help us better understand the real numbers in some cases.They also have some very practical applications, including: * Electrical circuits - in AC, things like resistance, current, and voltage acquire a phase angle, thus becoming complex numbers. * Quantum mechanics - the probability amplitude is described with a complex number. As a result, complex numbers basically permeate all of quantum mechanics.
Among other things, complex numbers play an important role:* In electrical circuits - quantities in AC circuits are described by complex numbers. * In quantum mechanics - the "probability amplitude" is an important concept in quantum mechanics, and it is described by a complex number. * In art - for example, the Mandelbrot set is based on calculations with complex numbers.
One operation that is used a lot in quantum mechanics is taking the absolute value of the square of a complex number. This is equivalent to multiplying the complex number by its complex conjugate - and doing this is simpler in practice.
The real numbers together with the imaginary numbers form a sort of vector. What these complex numbers (complex means the combination of real and imaginary numbers) represent depends on the specific situation. Just as there are situations where it doesn't make sense to use negative numbers, or fractional numbers, in many common situations it doesn't make sense to use complex numbers. In an electrical circuit (specifically, AC), the real numbers might represent resistance, while the imaginary number represent reactance - and voltages and currents are also represented by complex numbers, with the angle of the complex number representing how much one quantity is ahead or behind another quantity (the "phase angle"). In quantum mechanics, the complex numbers might not represent anything (perhaps they don't, I am not sure...), but they are useful for calculations.
electrical engineers and quantum mechanics use them.
Complex numbers are theoretically interesting; they help us better understand the real numbers in some cases.They also have some very practical applications, including: * Electrical circuits - in AC, things like resistance, current, and voltage acquire a phase angle, thus becoming complex numbers. * Quantum mechanics - the probability amplitude is described with a complex number. As a result, complex numbers basically permeate all of quantum mechanics.
Some of the jobs that use complex conjugates include quantum mechanics, electrical engineers and physicists. Complete understanding of generators and motors require the knowledge of imaginary numbers.
Among other things, complex numbers play an important role:* In electrical circuits - quantities in AC circuits are described by complex numbers. * In quantum mechanics - the "probability amplitude" is an important concept in quantum mechanics, and it is described by a complex number. * In art - for example, the Mandelbrot set is based on calculations with complex numbers.
One operation that is used a lot in quantum mechanics is taking the absolute value of the square of a complex number. This is equivalent to multiplying the complex number by its complex conjugate - and doing this is simpler in practice.
Physics (e.g., quantum mechanics, relativity, other subfields) makes use of imaginary numbers. "Complex analysis" (i.e., calculus that includes imaginary numbers) can also be used to evaluate difficult integrals and to perform other mathematical tricks. Engineering, especially Electrical Engineering makes use of complex and imaginary numbers to simplify analysis of some circuits and waveforms.
no
The real numbers together with the imaginary numbers form a sort of vector. What these complex numbers (complex means the combination of real and imaginary numbers) represent depends on the specific situation. Just as there are situations where it doesn't make sense to use negative numbers, or fractional numbers, in many common situations it doesn't make sense to use complex numbers. In an electrical circuit (specifically, AC), the real numbers might represent resistance, while the imaginary number represent reactance - and voltages and currents are also represented by complex numbers, with the angle of the complex number representing how much one quantity is ahead or behind another quantity (the "phase angle"). In quantum mechanics, the complex numbers might not represent anything (perhaps they don't, I am not sure...), but they are useful for calculations.
No, it is not necessary.
To effectively simulate traversable wormhole dynamics on a quantum processor, researchers can use quantum algorithms and techniques to model the complex interactions and properties of wormholes. By leveraging the principles of quantum mechanics, such as superposition and entanglement, scientists can create simulations that accurately represent the behavior of traversable wormholes in a quantum computing environment.
The no communication theorem in quantum mechanics states that it is impossible to use quantum systems to communicate faster than the speed of light. This is significant because it sets a fundamental limit on how information can be transmitted in the quantum world, impacting our understanding of the nature of reality and the possibilities of quantum technologies.
The physicist conducted groundbreaking research in the field of quantum mechanics.