AQA FP1 - Complex Numbers

Hey guys, been trying to figure out this question for a while and can't seem to get it. I've done the first part of the question, getting p = -8 and q = 9, and checking the answers that looks right.

However I'm kinda stuck on part B now. The sum of roots I got was 3-7i by doing -b/a. I don't know if that's right and to be honest, I have no idea where to go from there.

Can anybody give me a hint or some other way I could find the answer? Any help would be appreciated.

Question:

Reply 1

Swayum

Sum of the roots is 3 + 7i, I'll assume you made a typo. If not, reply back.

You're given that one root is 2 + 5i. If we call the other root z', then

2+5i + z' = 3 + 7i... find z'...

To answer the very last part, what do you notice about the coefficients of the quadratic?

(edited 13 years ago)

Reply 2

nuodai

I haven't checked your answer to part (a) so I'll assume it's correct.

For part (b) you know that

\alpha + \beta = 3+7i

(where

\alpha,\beta

are the roots), but you know that one of the roots is equal to

2+5i

, so

\beta

must be... [you do this bit].

As for the reason why this isn't the complex conjugate, you should know this. Otherwise, think about when you would expect the roots to be conjugate. [All else failing, consult your textbook; that or someone will probably jump in and tell you anyway, but it's much more fun to find out for yourself.]