NavList:

David,

        Although your post was written half in jest let me give you a straight-faced answer. The thesis you mention was written in 2020 but is largely a rehash of earlier work.

Complex numbers can be used in celestial navigation and other fields in which there are spherical coordinates. They have 2 independent parts so there enough degrees of freedom to encapsulate latitude and longitude in a single complex number. Trigonometric calculations are then transformed into simple arithmetic with complex numbers. It turns out that coordinate transformations of the sphere (e.g. HA, Dec to Alt, Az) take a particularly simple form. I pointed this out in a paper in 1984 "Applications of complex analysis to spherical coordinate geometry", Quarterly Journal of the Royal Astronomical Society, 25, 126–136. https://ui.adsabs.harvard.edu/link_gateway/1984QJRAS..25..126S/ADS_PDF

Having attended a conference Mystic Seaport that Frank Reed orgainized in 2008(?) I extended this to Celestial Navigation. The write up was attached to my first ever Navlist post https://navlist.net/twobody-computed-fix-Stuart-oct-2009-g10015 (That paper appeared print in NAVIGATION: Journal of the Institute of Navigation 56 221-227.)
I gave a talk on it at Frank's Mystic Seaport conference in 2010 https://navlist.net/Materials-from-Navigation-Weekend-Talk-Stuart-jun-2010-g13201
A subsequent related paper is Great Circles and Rhumb Lines on the Complex Plane. The Journal of Navigation. 70 618–627.

I think the main problem preventing the widespread adoption of complex numbers in celestal navigation is a lack of familiarity and that the operations are not intuitive for most.

I looked at the 2020 thesis you mention and could immediately see that the figure and equations on pages 20 to 25 are copied directly that celnav paper from 2009. I don't know if a Master's thesis needs to include something new or just demonstrate a knowledge of a technical subject. I am cited but it's my 1984 paper that is referenced.

Quaternions are essentially a generalization of complex numbers but with 4 components. They behave in the same way as the Pauli matrices to which they are equivalent. There are a number equivalent formalisms for performing rotations which I summarize in the appendix to my 2009 paper. I did read that quaterions are used in computer gaming as an efficient way to perform image rotations. Think about that the next time you are playing Grand Theft Auto!

Regards,
Robin