Indicator function (complex analysis): Difference between revisions

Revision as of 18:52, 18 August 2024

Latest revision as of 15:57, 4 August 2025

(One intermediate revision by the same user not shown)

Line 29:

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>