Imaginary part

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The function

ℑ (z)

gives the imaginary 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)

:

ℑ (z) := b = z − z̅ 2 = r sin  θ,

where

z̅

is the complex conjugate of

z

.
For example,

ℑ (3 + 2√   − 5 ) = 2√  5

.

A few sequences in the OEIS involve imaginary parts, such as for example A013629, floor of imaginary parts of nontrivial zeros of Riemann zeta function.

Compare real part.