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# Mathematics Club

## May 16 @ 4:00 PM - 5:00 PM PDT

Free**The ANGLE BONE’S CONNECTED TO THE MATRIX BONE…**

A note about our next *WALK DOWN A LOGIC CHAIN OF CONNECTEDNESS*:

For Mathematics Club of Science Circle at 4 PM PDT on Thursday 16.May 2024 in the Maths Dojo, we are going to continue our ** EXPLORATION** of the

**, beginning with deriving a formula for the SUM OF ANGLES for trigonometric functions, SIN and COS. With this very useful result, we can look at 2×2 matrices that cause PURE ROTATION in the plane when multiplied by a 2×1 column matrix as a matrix representation of a planar vector. We will also apply the SUM OF ANGLES formulae to show how even this calls out for the invention of the pure IMAGINARY NUMBER, i (in which”i” ^2 = – 1) which extends the REAL NUMBERS to the field of COMPLEX NUMBERS. We will see how**

*ANATOMY of MATHEMATICS***de Moivre’s theorem**from 1707 emerges:

for any complex number with a given angle α, de Moivre’s theorem relates that complex number to the **n**th power to a complex number of angle = **n** * α. At the conclusion, a challenge will be tossed out to our Maths Club participants to prove this theorem by the PRINCIPLE of INDUCTION. We will plan on revisiting this with an inductive proof of de Moivre’s Theorem the following week (23.May 2024).

In MATHEMATICS, it makes things generally easier to KEEP IT REAL, but DON’T FORGET TO BRING YOUR IMAGINATION because IMAGINARY NUMBERS EXIST just as surely as the number days in a week exist.

We hope to see you there!

– Tagline, tour guide and Sensei of Maths dojo