Real part

This article page is a stub, please help by expanding it.

The function

ℜ (z)

gives the real part of a complex number

z = r  e i θ = r cos  θ + i r sin  θ = a + i b = ℜ (z) + i ℑ (z)

:

ℜ (z) := a = z + z̅ 2 = r cos  θ,

where

z̅

is the complex conjugate of

z

.
For example,

ℜ (3 + 2√   − 5 ) = 3

.
The real part of a zero of the Riemann zeta function is either an even negative integer (for trivial zeros) or

1 2

(for the non-trivial zeros, if the Riemann hypothesis is true, otherwise greater than 0 but less than 1).

Compare imaginary part.