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 *c*_{1} and *c*_{2} is defined
to be:

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

Multiplication of two complex numbers *c*_{1} and *c*_{2} is defined
to be:

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