Building complex functions out of real parts
The article discusses the computation of complex functions using real parts, referencing equations from Henry G. Baker. It highlights the author's process of verifying these equations through Python code and the implications of branch cuts in mathematical identities. The post reflects on the deeper questions surrounding the definitions of functions in calculus education.
- ▪The author explores computing sine and cosine of complex numbers using real functions.
- ▪Equations from Henry G. Baker are utilized and verified with Python code.
- ▪The article addresses complications with branch cuts in mathematical identities.
Opening excerpt (first ~120 words) tap to expand
Building complex functions out of real parts Posted on 22 May 2026 by John A couple months ago I wrote about how to compute the sine and cosine of a complex number using only real functions of real variables using the equations You can do something analogous for all the elementary functions, though some of the equations are quite a bit more complicated than the ones above. See the equations here. The equations come from a paper by Henry G. Baker, cited in the linked page. I wrote up Baker’s equations in LaTeX, then used ChatGPT to generate Python code from the LaTeX to numerically verify the equations and my typesetting of them. This caught a few typos on my part. The test code evaluated the equations at points from each quadrant.
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Excerpt limited to ~120 words for fair-use compliance. The full article is at John D. Cook | Applied Mathematics Consulting.
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