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Complex Numbers

A complex number is a number of the form a + i*b, where a and b are real numbers, and i is defined to be the square root of negative one. Addition of two complex numbers c1 and c2 is defined to be:

c1 = a1 + i*b1

c2 = a2 + i*b2

c1 + c2 = a1 + a2 + i*(b1 + b2)

The complex conjugate of a complex number c, denoted c* is defined to be:

c = a + i*b

c* = a - i*b

Multiplication of two complex numbers c1 and c2 is defined to be:

c1 = a1 + i*b1

c2 = a2 + i*b2

c1*c2 = a1*a2 - b1*b2 + i*(a1*b2 + a2*b1)

Euler's Formula for complex numbers states that eix = cos x + i*sin x, this relationship is used in the discrete Fourier transform of Shor's algorithm.


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Matthew Hayward - Quantum Computing, Shor's Algorithm, and Parallelism GitHub Repository