Solve Quadratic Equation with Imaginary Terms: (3-i)^2(3+i)/2-i

[soccerjayl]

Could not form a complete answer on this. Yes i know i need help with LaTeX printing, but please work with me for now:

Write in Standard Form.

(3-i)$$^2$$(3+i)
___________________
2-i


First i made the zeros part of the factorization, ie

(x-(3-i)$$^2$$)(x-(3+i)
________________________
(x-(2-i))

but I'm lost, how do i make the form Ax + By + C out of this??

 

[robphy]

"Standard form" meaning "a+bi" ?

 

[soccerjayl]

"Standard form" meaning "a+bi" ?

sorry...

i'm guessing it is...i was assuming it was a harder question than it really was?

by my calculations though, 14 + 2i is the correct answer, eh?

 

[soccerjayl]

Another question i had trouble on...

Find the remainder:

$$x^4-3x^2+5x-1$$ divided by $$x^2-3$$

The remainder theorem being if x-k is dividend
f(k)=remainder

considering there are two parts to $$x^2-3$$ (plus OR minus square root of 3), how do i go about doing the problem?

 

[shmoe]

You can use long division. I first thought to write an example, but gah, that wouldn't be fun. Google "polynomial division" and you'll get many pages, the first one is good:

http://www.sosmath.com/algebra/factor/fac01/fac01.html

 

[soccerjayl]

as much as i like viewing the basics of the problem, no thanks

do the problem

using long division, i get r= 5x-1 over x^2-3

are you going to agree, or are you going to give it more thought

 

[shmoe]

I assumed since you asked for an approach on how to tackle the problem you didn't know or had forgotten about polynomial long divison and thought a link to an example might be usefull to you. My mistake I guess.

Since you appear to be hoping someone will do your work and check your answer, I'll pass.

 

[soccerjayl]

Well if you weren't lazy, you'd see it wasnt an average problem...

Its no good having the basics when you need the higher level guides to harder problems...doh

but as you are still lazy in being unwilling to agree with me after I've shown my own answer, fine pass, but if i had wanted the basics, trust me, id have "google"d originally

so thanks for your help

*******

 

[shmoe]

On the contrary, yours a basic problem of polynomial division. The link I provided quotes the division algorithm and provides a fine example immediately after. This example is exactly of the type of problem you are attempting to solve. After the example they even explain how you can check your answer. If you knew these basics as you claim, why did you ask how to approach the problem?

As for being lazy, I did provide you with a link and I did take the time to skim it and see that it was indeed very relevant to your problem. So yea, I took my own time to do this for you, but feel free to call me lazy. Note that my refusal to check your work came after your curt demand "do the problem". Think about that.

 

[soccerjayl]

It was not a curt demand. I was only telling you that if you did the problem, you would recognize that it was different. It wasn't a DO THE PROBLEM FOR ME! sorry for the misunderstanding. As far as the basics, maybe my advanced problems are your basics, who knows. But thanks for your help, i do appreciate it.

 

[Zurtex]

I don't understand.

If you want to put it in the form, a + bi then why don't you just expand the numerator and multiply numerator and denominator by the denominators complex conjugate?

 

[modmans2ndcoming]

how is making you do your own work being lazy on his/her part?

and that problem is pretty normal for polynomial division. this is a help forum, not a quick answer for kids who are in over their heads forum.

 

[modmans2ndcoming]

no matter where you are in mathematics, your advanced is always someone else's basics.

 

[shmoe]

It was not a curt demand. I was only telling you that if you did the problem, you would recognize that it was different.

Fair enough, but you should realize that your problem is not any different than any other polynomial division problem (I have done it btw). You were obviuosly capable of doing this division. Have a look at the link I gave and tell me if there's anything fundamentally different about your problem that isn't covered by the standard division algorithm (I mean this, you should be able to compare the problems if you think they're different).

By "basic" I meant "standard", not that it was easy from everyones viewpoint. Believe me, I had a professor once who proclaimed everything was easy, even if we were talking about some pretty complicated abstract algebra (it was a Galois theory course)...it's easy if you've done it before and taught it several times, but wasn't so easy for the student!