I wouldn't know right of the bat, that it would factorize as that, how did you work it out? Also once I've solved the quadratic etc, and am readjusting the arguments, why is it + pi and not + 2pi?

Thanks.

Reply 5

Mr M

Study Forum Helper

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Original post by Music99

How did you work out what the middle term will be?

Seriously?

The coefficient of z^2 needs to be -1.

We have 1z^2 + 1z^2 so we need to subtract 3z^2.

Reply 6

Music99

OP

4

Original post by Mr M

Seriously?

The coefficient of z^2 needs to be -1.

We have 1z^2 + 1z^2 so we need to subtract 3z^2.

Ah, my bad. It's getting late, and I'm having to teach myself FP3 and FP2 :P.

Original post by Music99

Ah, my bad. It's getting late, and I'm having to teach myself FP3 and FP2 :P.

Ah ok. I was assuming more knowledge than that. I thought this was an undergraduate thread - I've just noticed Sixth Form in the title.

Reply 8

Music99

OP

4

Original post by Mr M

Ah ok. I was assuming more knowledge than that. I thought this was an undergraduate thread - I've just noticed Sixth Form in the title.

Well I am technically an undergrad, but transferring unis to York (fingers crossed), but have to do A-level further maths :P.

Original post by Music99

I wouldn't know right of the bat, that it would factorize as that, how did you work it out? Also once I've solved the quadratic etc, and am readjusting the arguments, why is it + pi and not + 2pi?

Thanks.

I think the way you were supposed to approach this is to complete the square on the disguised quadratic.

z^4 -z^2 +1=0

(z^2 - \frac{1}{2})^2 - \frac{1}{4} + 1 = 0

z^2 = \frac{1}{2} \pm \frac{i \sqrt{3}}{2}

Now convert this pair of solutions to polar form and find the square roots to obtain four solutions and then write it as a set of four linear factors.

Original post by Music99

Well I am technically an undergrad, but transferring unis to York (fingers crossed), but have to do A-level further maths :P.

I see. Do you read mathematics at the moment? Where are you now?

Reply 11

Music99

OP

4

Original post by Mr M

I see. Do you read mathematics at the moment? Where are you now?

I do, It's good just obviously some of the further maths stuff I haven't covered before. I'm at Brighton at the moment, and hopefully transferring to York.

Complex number question

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