Exploring Radio Mathematics (My November 2020 QST Article)

The November issue of QST contains my article “Exploring Radio Mathematics.” QST invited me to write it over a year ago. I want to thank the editorial staff at QST for suggesting that I write this article. By the way, they also asked me to write the article, published several months ago, about the symbolism in the new FCC logo.

Click here to see the updated QST article as it appears now on the QST online website. Updates have been incorporated. Thanks especially to Kai Siwiak, KE4PT, an ARRL Technical Advisor and QST Contributing Editor, for his review and updates.

Please understand, and this is important, that I never got a proof to review. That’s really bad, particularly for an article with lots of mathematics, because some mistakes crept in during editing, plus I made a mistake I was hoping to fix during the proofing process that is now in the final article. I have received numerous emails pointing out my mistakes (and my shortcomings!), all saying essentially the same thing.

This page is my response to the mistake-plagued article plus my response to the various comments I received. When things settle down a bit I will also do a video exploring the mistakes, plus another video that uses the corrected article as a script.

The article was prompted by my Amateur Extra Class training video on Radio Mathematics. So this is Extra-class material and is not simple. I don’t think it’s conceptually difficult, but then again I have a Bachelor’s degree in Mathematics and a Master’s Degree in Engineering.

First, let me own up to the error I created. I stated on page 35 that i^^2 (i squared) = sqrt(-1) (square root of -1). This is certainly wrong. It should have read that i^^2 (i squared) = -1 (minus one).

Now comes the weird one. The article says in the same paragraph that j equals minus i. It most certainly does not. The letter i is used by mathematicians and the letter j is used by engineers because for engineers, i is reserved for current. In other words i and j are identically equal and are one and the same thing.

There is also the issue of how to represent numbers in polar coordinates. It should be a magnitude (length) followed by an angle, such as 25/45 degrees. The entire article as published leaves out the underscore, and there is at least one situation where the forward slash (/) is used in its normal sense of division.

There is also a case where what should be 4**2 (four squared) is simply rendered 42.