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Euler's identity in ASTRON Tele-course on complex numbers

Submitter: Ronald Halfwerk
Description: "In the year 1777, Leonhard Euler and his assistants submitted more than 50 articles to the Imperial Academy of Sciences of St. Petersburg. In fact Euler, already blind for more than five years, and his companions wrote articles too fast for the Academy's publishers. So it took until 1793 for them to be printed, sixteen years after they were written, and these articles apparently escaped being read before the Academy". (Copied from: How Euler did it - Introduction to Complex Variables, Ed Sandifer. MAA.org )

Complex numbers complete our number system, and offer many advantages. The main point of these Euler papers, which include what is said to be the most beautiful formula in mathematics, was to show that calculus with complex numbers is possible, and that it is just an extension of calculus with real numbers.

Complex numbers have both an amplitude and a phase. This makes them ideal for describing electrical signals, which can be thought of as a superposition of sinusoidal functions. Alternatively, a complex number "a+jb" can be thought of as having a "real" part (a) and an "imaginary" part (jb), where "j" is the square root of -1. (Mathematicians and physicists like to use the letter "i" instead). The more everyday "real" numbers only consist of the first part, and are therefore incomplete.

In the popular 3-day ASTRON course on Applied Radio Frequency (RF) technology (Dutch: Cursus Toegepaste RF-techniek), which was held again on November 5-7, the use of complex numbers is unavoidable. For the benefit of participants, we offered a preparatory "Live Tele course" on Complex calculus, in order to allow our students to remotely refresh their knowledge in this area beforehand. Our students did login to an EVO session for this purpose.

ASTRON has obtained permission from the Open University Netherlands to use one of their modules on Complex numbers for the purpose of this Tele-course. Our own Koos Kegel acted as lecturer. In the pictures, Koos is armed with head-set and electronic pencil to guide the students along.

Copyright: fotos (c) 2012 ASTRON
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