Comments on: Imaginary Multiplication vs. Imaginary Exponents

By: Grigory

Grigory — Tue, 10 Jun 2025 10:00:55 +0000

Brilliant explanation, as always! I have a side note, however. It was also difficult for me to understand how and why "The orbit doesn't get faster". However, I've found the following insight from physics. The exponent is a force. Why doesn't a perpendicular force make you spin faster and faster? However, that's the same, say, with the Moon. The gravitational force of Earth is applied perpendicular to its direction, however, it doesn't make it spin around Earth faster and faster. The force here is unable to change its angle speed (lets assume the orbit is circular), its whole effect is in changing direction only!

By: Amine

Amine — Thu, 10 Aug 2023 17:57:53 +0000

I watched a video of an MIT math professor Gilbert Strang that explains how to obtain e^x (the function/polynomial that is equal to its derivative), we start with 1 if we derive it we obtain 0 but 0 is always present in both the the function and its derivative. Then we want 1 in the derivative so we add x to f(x), now the equation is 1 + x but x is still missing in the derivative, so we continue, we need to derive something that give us x and it's (x^2)/2 so now the function is 1 + x + (x^2)/2. the derivative lacks the (x^2/2) so we have to add something when derived will output (x^2/2) and it's x^3 / (1 * 2 * 3). the pattern for the other terms of the exp function is x^n/n! this explains taylor series too ! the video : https://www.youtube.com/wat...

By: 이동근

이동근 — Fri, 16 Dec 2022 15:20:29 +0000

Thanks! hands down the best explanation i've ever seen

By: Arturo Barrera

Arturo Barrera — Mon, 10 Jun 2019 21:12:13 +0000

6/10/2019

Kalid,:

I do not have a degree in math, so take my comment in that light. Your website is enlightening, although I am a little confused about your explanation of i as an exponent. Your diagram seems to indicate when raising a number to the i th power, graphically there is a perpendicular rotation at the end of "growth". I played around with geogebra and reached the following conclusion. Wouldn't it be simpler to say:

"To calculate any real number n to the i th power, imagine a segment connecting the origin (0,)0) to point (1,0); rotate this segment by ln(n) radians. The result will be at the tip of the rotated segment, or at cos (ln(n))+ i*sin (ln(n)) . "

See https://www.geogebra.org/cl...

A. Bsrrera