Complex numbers

Original post by bubblegum21

I need to divide x^3 + 2x^2 + wx + u by x^2 - 2x where w= 4i + 2 and u=0. I don't know how to go about it. I know you're supposed to use long division but after that I'm lost. Any suggestions?

If u = 0 then all your terms are divisible by x, so you can cancel that out to start with and just concentrate on dividing by x - 2.

Reply 2

Original post by davros

If u = 0 then all your terms are divisible by x, so you can cancel that out to start with and just concentrate on dividing by x - 2.

I forgot to mention that there's a +2 at the end of x^2-2x. Any suggestions?

Reply 3

Original post by bubblegum21

I forgot to mention that there's a +2 at the end of x^2-2x. Any suggestions?

Use long division, not sure what the problem with that is.

What is the full question?

Reply 4

Original post by james22

Use long division, not sure what the problem with that is.

What is the full question?

Divide x^3 + 2x^2 + wx + u by x^2 -2x + 2 where w= -4i -2 and u=0. I am not sure how to use long division when complex numbers are involved

Reply 5

Original post by bubblegum21

Divide x^3 + 2x^2 + wx + u by x^2 -2x + 2 where w= -4i -2 and u=0. I am not sure how to use long division when complex numbers are involved

Same as normal long division. It's no different.

Reply 6

Original post by bubblegum21

Divide x^3 + 2x^2 + wx + u by x^2 -2x + 2 where w= -4i -2 and u=0. I am not sure how to use long division when complex numbers are involved

So let's be quite clear about this. The FULL question you've been asked is:

Divide

x^3 + 2x^2 -(2 + 4i)x

x^2 - 2x + 2

Is there a reason why you introduced the unnecessary w and u? I'm just concerned we're missing the point of the question here :smile:

Reply 7

Original post by davros

So let's be quite clear about this. The FULL question you've been asked is:

Divide

x^3 + 2x^2 -(2 + 4i)x

x^2 - 2x + 2

Is there a reason why you introduced the unnecessary w and u? I'm just concerned we're missing the point of the question here :smile:

thats correct. Well the first part of the question is to determine the values of w and u which I found by solving simultaneously. That bit is the second part

Reply 8

Original post by bubblegum21

thats correct. Well the first part of the question is to determine the values of w and u which I found by solving simultaneously. That bit is the second part

Can you please post the full question still?

Reply 9

Original post by bubblegum21

thats correct. Well the first part of the question is to determine the values of w and u which I found by solving simultaneously. That bit is the second part

As per james22, can we please see the full question so we know what the purpose behind the question is?

Reply 10

Original post by james22

Can you please post the full question still?

I have attached the question

(edited 9 years ago)

image.jpg46.4KB

Reply 11

Original post by bubblegum21

I have attached the question

What are you trying to use polynomial division on this?

Reply 12

Original post by james22

What are you trying to use polynomial division on this?

To find the other root. As 1+i is a root, so is it's conjugate 1-i. As it is a cubic root there is one other root left. So to find it we were taught to use polynomial division to f the last root

(edited 9 years ago)

Reply 13

Original post by bubblegum21

To find the other root. As 1+i is a root, so is it's conjugate 1-i. As it is a cubic root there is one other root left. So to find it we were taught to use polynomial division to f the last root

Given that you're told in part (a) that the coefficients are real, how have you ended up with an 'i' in your w???

This is why we asked to see the full question :smile:

Reply 14

Original post by davros

Given that you're told in part (a) that the coefficients are real, how have you ended up with an 'i' in your w???

This is why we asked to see the full question :smile:

Thats a fair point! As I got w= -4i-2, does the i just disappear and the answer is -6?

Reply 15

Original post by bubblegum21

Thats a fair point! As I got w= -4i-2, does the i just disappear and the answer is -6?

No. It means you have gone wrong in your working.

Reply 16

Original post by bubblegum21

Thats a fair point! As I got w= -4i-2, does the i just disappear and the answer is -6?

No it means you've got the wrong value for w!

(The point here is that from experience I know that it is highly unusual that you're going to be asked to divide a polynomial with complex terms by another polynomial with real terms. Therefore I felt that your original post had to be 'suspect' in some way :smile:

)

Reply 17