Real and Imaginary Parts
The article discusses the implementation of functions of a complex variable in terms of real variables. It highlights the significance of finding real and imaginary parts of complex functions and their applications in mathematics. The equations presented can be useful for creating math libraries that do not support complex numbers.
- ▪The article is based on notes by Henry Baker regarding complex variables.
- ▪It explains how to express complex functions in terms of real-valued functions.
- ▪The real and imaginary parts of a complex analytic function are harmonic functions.
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Record
| Original publisher | John D. Cook | Applied Mathematics Consulting |
| Canonical URL | https://www.johndcook.com/blog/2026/05/23/real-and-imaginary-parts/ |
| Publication time | Thu, 28 May 2026 01:32:48 +0000 |
| Retrieval time | 2026-05-28T01:58:06.865Z |
| Last seen | 2026-05-28T01:58:06.865Z |
| Headline source | Publisher (no WeSearch rewrite) |
| Excerpt source | publisher body |
| Excerpt method | First ~120 words (~800 chars) of extracted publisher body, fair-use limited. |
| Summary | WeSearch · cerebras-chat (WeSearch summarizer) |
| Summary source text | contentText |
| Citation coverage | Summary is a WeSearch-generated derivative; primary citation is the original publisher URL. |
| Cluster | KBkAWJ9DnYRZ · 2 stories |
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| Ranking reason | Story pages are not engagement-ranked. Hub feeds use recency, with optional source-diversified chronological ordering (cap consecutive stories per source). No personalized ranking. |
| Publisher visit | Yes — open original |
| Substitutes article? | No — link-out required for full text |
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| Indexing | May the item be indexed (stored, ranked, made findable)? | Allowed |
| Snippet | May a short excerpt of the publisher's text be shown? | Allowed |
| AI summary | May WeSearch generate its own short summary of the article? | Limited |
| Retrieval / RAG | May the content be exposed for third-party retrieval-augmented generation? | Not asserted |
| Model training | May the content be used to train AI models? | Not asserted |
| Commercial reuse | May the content be reused commercially? | Not permitted |
Basis: Derived from the published RSS/Atom feed. Contact: [email protected]. Reviewed: 2026-07-24.
Opening excerpt (first ~120 words) tap to expand
Real and imaginary parts Posted on 23 May 2026 by John The previous post announced some notes I wrote up based on an article by Henry Baker implementing functions of a complex variable in terms of functions of a real variable. That is, it finds functions u(x, y) and v(x, y) such that f(x + iy) = u(x, y) + i v(x, y) where x, y, u, and v are all real-valued. Not only that, but if f is an elementary function, so are u and v. Here “elementary” has a technical meaning, but essentially it means functions that you could evaluate on a scientific calculator. A couple of the functions might be unfamiliar, such as sgn and atan2, but there are no functions like the gamma function that are defined in terms of integrals.
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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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