The Student Room Group

Complex numbers help

Hi,
I have got to complete this sheet for tomorrow. I don't have a clue how to work most of them out. So far I have only managed to 4(a) and 5(i). Other than that I havent been able to do any. I really need help as she will 'kill' me if i hand it in all wrong.

I would really really appreciate any/all hep. Thank you.

maths.JPG
Reply 1
Original post by Alexia_17
Hi,
I have got to complete this sheet for tomorrow. I don't have a clue how to work most of them out. So far I have only managed to 4(a) and 5(i). Other than that I havent been able to do any. I really need help as she will 'kill' me if i hand it in all wrong.

I would really really appreciate any/all hep. Thank you.

maths.JPG

Please post your attempt for the first question you can't do and show us where you're stuck.
Original post by Alexia_17
...


A better quality image would be useful. Even when I download that and blow it up, I have to guess at what parts of it say.
Reply 3
Original post by Notnek
Please post your attempt for the first question you can't do and show us where you're stuck.


I don't know where to start and I have been staring at the page for half an hour. I have nothing writtn down on my page for 4(b-h) and only a little bit for 5 and 7

maths 1.JPG
Reply 4
Original post by ghostwalker
A better quality image would be useful. Even when I download that and blow it up, I have to guess at what parts of it say.



sorry,

maths 1.JPG
Reply 5
Original post by Alexia_17
I don't know where to start and I have been staring at the page for half an hour. I have nothing writtn down on my page for 4(b-h) and only a little bit for 5 and 7

maths 1.JPG

For 4b) you need to first solve the quadratic using the quadratic formula. Try that and please post your working if you get stuck.

Also please make your images bigger and clearer. If you are having trouble posting images on TSR then try an alternative method.
Reply 6
I have now managed to complete quesion 8 but I am still struggling on the rest.
Reply 7
Original post by Notnek
For 4b) you need to first solve the quadratic using the quadratic formula. Try that and please post your working if you get stuck.


I have gotten this far but i dont know what to do next
maths 1.JPG
Reply 8
Original post by Alexia_17
I have gotten this far but i dont know what to do next
maths 1.JPG

If α\alpha is a root of a polynomial then (xα)(x-\alpha) must be a factor of the poynomial.

E.g. for x2x6x^2-x-6, the two roots are 3, -2 and it factorises to give

(x+2)(x3)(x+2)(x-3)

I think you know this already - you just need to apply it to a quadratic with complex roots.
Reply 9
Okay, I think I have got the hang of 4 now. Does anyone have an idea about question 7 though?
Original post by Alexia_17
Okay, I think I have got the hang of 4 now. Does anyone have an idea about question 7 though?

z* is the complex conjugate, so it is a -bi rather than a +bi
Reply 11
Original post by Alexia_17
Okay, I think I have got the hang of 4 now. Does anyone have an idea about question 7 though?

From squinting at your working I think you've started fine. Now try writing the left-hand-side in the form x+iyx+iy.
Reply 12
@alexia17 There's a quick way to do Q7 by using

zw=zw\displaystyle \left|\frac{z}{w}\right| = \frac{|z|}{|w|} *

and realise that c2+d2c^2+d^2 is the modulus squared of c+dic+di.

* But I don't know if you know this rule.

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