# Complex numbers in quantum theory

• ## What are complex numbers in quantum theory?

A complex number comprises a real number plus an imaginary number, which is a multiple of the square root of -1.
While the mathematics of complex numbers underlies modern quantum theory, it is also possible to describe the quantum world purely in terms of real numbers.Jan 11, 2022.

• ## What is the role of complex analysis in quantum mechanics?

Quantum Mechanics:
Complex analysis is used to solve the CPT Theory (Charge, Parity and Time Reversal), as well as in conformal field theory and in the Wick's Theorem.
Complex variables are also a fundamental part of QM as they appear in the Wave Equation..

• Complex numbers is a kind of two-dimensional vectors whose components are the so-called real part and imaginary part.
The real part usually corresponds to physical quantities while the imaginary part is a purely mathematical construction.
• Qubits Require Complex Numbers.
Let's think about why we need complex numbers to describe qubits.
Essentially it boils down to the fact that rotation in the Euclidean plane using real numbers reduces to simple multiplication using complex numbers.
In standard quantum theory, the state of a physical system is represented by a vector (a quantity with a magnitude and direction) of complex numbers called the wave function. Physical properties, such as the speed of a particle or its position, correspond to tables of complex numbers called operators.
Standard quantum theory, with its complex numbers, has a convenient rule that makes it easy to represent the wave function of a quantum system composed of many independent parts—a feature that these other versions lack.

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