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]

[581] **Forster Otto**: “Analysis 1, Differential- und Integralrechnung einer Veränderlichen”, Vieweg Studium, 1983