Complex number

A complex number has a real part and an imaginary part, commonly written $z=x+iy$ with $i^2=-1$.

Complex numbers let functions vary in two real directions at once. Riemann's decisive step was to study the zeta function as a function of a complex variable; the Riemann Hypothesis then concerns the real parts of certain complex zeros.

See also: complex plane, real part, imaginary part, Riemann zeta function..