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## Proposition: Extracting the Real and the Imaginary Part of a Complex Number

Let $$z\in\mathbb C$$ be a complex number. Because by definition
$z:=\Re(z) + \Im (z) i$
and because from the definition of complex conjugate we have that
$z^*:=\Re(z) – \Im (z) i,$
it follows (by adding or subtracting both equations) that

$\Re(z)=\frac 12(z+ z^*)$
and that
$\Im(z)=\frac 1{2i}(z- z^*).$

| | | | | created: 2015-04-26 18:30:01 | modified: 2020-06-14 13:59:21 | by: bookofproofs | references: [581]