Hey, guys!
So, in my Introduction to Robotics class, we are supposed to solve, as a part of solving an example, this equation (page 12):
1/s+1/(s+2)+1/(s+6-2i)+1/(s+6+2i)=1/(s+1)
Now, the very next step we are given goes like this:
3s^4+32s^3+106s^2+128s+80=0
I do not understand how they got from the first equation to the second one. Can somebody here explain me that?

Again with the homework.

Boru

It would appear that FA doesn't have teachers or classmates.

https://pasteboard.co/OpS78RwMHcd4.png

https://pasteboard.co/TG8gsyJuDdwy.png

Easy algebra, as long as you know what to do with the i's.

In case this is new to you, i^2 = -1

(February 13, 2022 at 11:50 am)GrandizerII Wrote: https://pasteboard.co/OpS78RwMHcd4.png

https://pasteboard.co/TG8gsyJuDdwy.png

Easy algebra, as long as you know what to do with the i's.

In case this is new to you, i^2 = -1

Well, I do not know much about complicated numbers.

(February 13, 2022 at 12:19 pm)FlatAssembler Wrote:

(February 13, 2022 at 11:50 am)GrandizerII Wrote: https://pasteboard.co/OpS78RwMHcd4.png

https://pasteboard.co/TG8gsyJuDdwy.png

Easy algebra, as long as you know what to do with the i's.

In case this is new to you, i^2 = -1

Well, I do not know much about complicated numbers.

That’s true. You don’t even know that they’re called ‘complex numbers.’

Boru

(February 13, 2022 at 12:21 pm)BrianSoddingBoru4 Wrote:

(February 13, 2022 at 12:19 pm)FlatAssembler Wrote: Well, I do not know much about complicated numbers.

That’s true. You don’t even know that they’re called ‘complex numbers.’

Boru

What's the difference?

(February 13, 2022 at 12:28 pm)FlatAssembler Wrote:

(February 13, 2022 at 12:21 pm)BrianSoddingBoru4 Wrote: That’s true. You don’t even know that they’re called ‘complex numbers.’

Boru

What's the difference?

The correct term is 'complex numbers', just like the correct term for fractions is 'rational numbers'.  You don't get to change to a different adjective even if it would be correct in ordinary language.

And, really, the only thing you need to know about complex numbers is that i^2 =-1. All the rest of algebra works the same (although order properties don't exist).

(February 13, 2022 at 12:28 pm)FlatAssembler Wrote:

(February 13, 2022 at 12:21 pm)BrianSoddingBoru4 Wrote: That’s true. You don’t even know that they’re called ‘complex numbers.’

Boru

What's the difference?

The difference lies in the imaginary.

(March 19, 1975 at 12:04 pm)polymath257 Wrote: And, really, the only thing you need to know about complex numbers is that i^2 =-1. All the rest of algebra works the same (although order properties don't exist).

Complex conjugates?