ThmDex – An index of mathematical definitions, results, and conjectures.

ThmDex – An index of mathematical definitions, results, and conjectures.

Result R5123 on D786: Standard natural complex exponential function

Formulation 0

Let $\theta \in \mathbb{R}$ be a D993: Real number.
Let $i$ be the D371: Imaginary number.

Then \begin{equation} |\exp (i \theta)| = 1 \end{equation}

Proofs

Proof 0

Let $\theta \in \mathbb{R}$ be a D993: Real number.
Let $i$ be the D371: Imaginary number.

This result is a particular case of R5124: Modulus of complex number polar representation. $\square$