Hi.
Recently there was a video on youtube that demonstrates how
to use complex numbers to solve a geometry problem.

https://www.youtube.com/watch?v=_hmNwG7Ppyo

It's an interesting approach, but I wonder if complex numbers are
really all that helpful.
Supposedly complex numbers provide a kind of computational
short-cut for rotation, but I don't see that much benefit compared
to doing something like (cos(a)P.x - sin(a)P.y, sin(a)P.x + cos(a)P.y)
to rotate a point P around the origin by an angle a.

https://www.desmos.com/calculator/ngxzaolblg

on 8/31/2022, sobriquet supposed :
> Hi.
> Recently there was a video on youtube that demonstrates how
> to use complex numbers to solve a geometry problem.
>
> https://www.youtube.com/watch?v=_hmNwG7Ppyo
>
> It's an interesting approach, but I wonder if complex numbers are
> really all that helpful.
> Supposedly complex numbers provide a kind of computational
> short-cut for rotation, but I don't see that much benefit compared
> to doing something like (cos(a)P.x - sin(a)P.y, sin(a)P.x + cos(a)P.y)
> to rotate a point P around the origin by an angle a.
>
> https://www.desmos.com/calculator/ngxzaolblg

The polar form as opposed to the rectangular form is not unique to the
complex plane. It is nice that pure phase (rotation) is independent of
magnitude for some kinds of calculations.

On Wednesday, August 31, 2022 at 2:22:27 PM UTC-7, FromTheRafters wrote:
> on 8/31/2022, sobriquet supposed :
> > Hi.
> > Recently there was a video on youtube that demonstrates how
> > to use complex numbers to solve a geometry problem.
> >
> > https://www.youtube.com/watch?v=_hmNwG7Ppyo
> >
> > It's an interesting approach, but I wonder if complex numbers are
> > really all that helpful.
> > Supposedly complex numbers provide a kind of computational
> > short-cut for rotation, but I don't see that much benefit compared
> > to doing something like (cos(a)P.x - sin(a)P.y, sin(a)P.x + cos(a)P.y)
> > to rotate a point P around the origin by an angle a.
> >
> > https://www.desmos.com/calculator/ngxzaolblg
> The polar form as opposed to the rectangular form is not unique to the
> complex plane. It is nice that pure phase (rotation) is independent of
> magnitude for some kinds of calculations.

coefficients don't make imaginary quantities real....
Stop moving your i around it won't make you see anything real...