◀ ▲ ▶Branches / Numbersystemsarithmetics / Proposition: Extracting the Real and the Imaginary Part of a Complex Number
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
\[\Im(z)=\frac 1{2i}(z z^*).\]
Table of Contents
Proofs: 1
Mentioned in:
Definitions: 1
Proofs: 2 3
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References
Bibliography
 Forster Otto: "Analysis 1, Differential und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983