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Real part

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The function
ℜ (z)
gives the real part of a complex number
z = r  eiθ = r cos  θ + i r sin  θ = a + i b = ℜ (z) + i ℑ (z)
ℜ (z) := a =
z +
= r cos  θ,
is the complex conjugate of
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
(for the non-trivial zeros, if the Riemann hypothesis is true, otherwise greater than 0 but less than 1).

Compare imaginary part.