Indicator function (complex analysis): Difference between revisions

Revision as of 18:52, 18 August 2024

Revision as of 15:56, 4 August 2025

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Since the complex sine and cosine functions are [[Sine and cosine#Complex arguments|expressible]] in terms of the exponential, it follows from the above result that

:<math>

h_{\sin}(\theta)=h_{\cos}(\theta)= \begin{cases}left|\sin(\theta)|\right|

\sin(\theta), & \text{if } 0 \le\theta<\pi \\

-\sin(\theta), & \text{if } \pi \le \theta<2\pi.

\end{cases}

</math>