# Complex numbers in number theory

• ## Where do complex numbers appear?

Complex numbers arise from the need to express negative numbers' roots, which real numbers can't do.
This is why they reflect all the roots of polynomials.
Their use extends to different scientific branches, ranging from mathematics to engineering..

• ## Why do complex numbers appear in quantum mechanics?

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..

A complex number is a number that can be written in the form a + b i a + bi a+bi, where a and b are real numbers and i is the imaginary unit defined by i 2 = − 1 i^2 = -1 i2=−1. The set of complex numbers, denoted by C, includes the set of real numbers (R) and the set of pure imaginary numbers.

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