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# fp1 complex numbers watch

1. (Original post by timebent)
not sure if the method i used is called factor theorem or inspection
http://www.examsolutions.net/a-level...y/paper.php#Q5
but for this question if it gives me one complex number and there's 3 roots then i know it's got to be a pair

and i used inspection or factor theorem or whatever it's called and tried 2 and got lucky so where would i get my marks assuming that this is my working

because it has a pair

let

f(2)=8-32+44-20=0

therefore z=2 thus z-2 is a factor
It's called the factor theorem. I'm guessing what you could've done if you finished Chapter 1 you'd know this - solve a cubic equation. Find the quadratic equation which has the roots 3 + i and 3 - i.
Then, just do z-a or a variable and work out a by comparing the coefficients.

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2. (Original post by timebent)
not sure if the method i used is called factor theorem or inspection
http://www.examsolutions.net/a-level...y/paper.php#Q5
but for this question if it gives me one complex number and there's 3 roots then i know it's got to be a pair

and i used inspection or factor theorem or whatever it's called and tried 2 and got lucky so where would i get my marks assuming that this is my working

because it has a pair

let

f(2)=8-32+44-20=0

therefore z=2 thus z-2 is a factor
Try the method I posted. If you manage to find the quadratic equation which has the complex roots 3 +/- i, then I give you the next hint if you struggle to find the answer using my method.

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3. (Original post by timebent)
x
Also, according to the mark scheme you'd get full marks using factor theorem.

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4. (Original post by timebent)
not sure if the method i used is called factor theorem or inspection
http://www.examsolutions.net/a-level...y/paper.php#Q5
but for this question if it gives me one complex number and there's 3 roots then i know it's got to be a pair

and i used inspection or factor theorem or whatever it's called and tried 2 and got lucky so where would i get my marks assuming that this is my working

because it has a pair

let

f(2)=8-32+44-20=0

therefore z=2 thus z-2 is a factor
You have to justify it a bit better, because all of the coefficient of the cubic are real. For polynomials with real coefficients if the complex number is a root, then so is its complex conjugate .
The more formal way to find the real root is to recognise that is a factor of the cubic. If you expand this product out you will get a real quadratic factor.
5. (Original post by Chittesh14)
It's called the factor theorem. I'm guessing what you could've done if you finished Chapter 1 you'd know this - solve a cubic equation. Find the quadratic equation which has the roots 3 + i and 3 - i.
Then, just do z-a or a variable and work out a by comparing the coefficients.

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(Original post by Chittesh14)
Try the method I posted. If you manage to find the quadratic equation which has the complex roots 3 +/- i, then I give you the next hint if you struggle to find the answer using my method.

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(Original post by Chittesh14)
Also, according to the mark scheme you'd get full marks using factor theorem.

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Awesome thanks
(Original post by B_9710)
You have to justify it a bit better, because all of the coefficient of the cubic are real. For polynomials with real coefficients if the complex number is a root, then so is its complex conjugate .
The more formal way to find the real root is to recognise that is a factor of the cubic. If you expand this product out you will get a real quadratic factor.
ah i see, so if the coefficient of the cubic are real then if Z1 is a root so is its conjugate?
6. (Original post by timebent)
Awesome thanks

ah i see, so if the coefficient of the cubic are real then if Z1 is a root so is its conjugate?
Yeah, that's right.

A cubic equation can have:

Either; all three roots as real
Or, one root is real and the other two roots form a complex conjugate pair.

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7. (Original post by timebent)
Awesome thanks

ah i see, so if the coefficient of the cubic are real then if Z1 is a root so is its conjugate?
Also, I'm not sure if you tried my method. But, here is how I'd have done it:

First thing (if you're confused) - I worked out the quadratic equation which has those complex roots.

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8. (Original post by timebent)
Awesome thanks

ah i see, so if the coefficient of the cubic are real then if Z1 is a root so is its conjugate?
Yes.
9. (Original post by B_9710)
Yes.

Part (b)

I've come to so many equations and if I check the answer and sub he values, they all work. But, I can't get to the actual answer...

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10. (Original post by Chittesh14)
Also, I'm not sure if you tried my method. But, here is how I'd have done it:

First thing (if you're confused) - I worked out the quadratic equation which has those complex roots.

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hmm i'll have a look tomorrow i think i know what you've done
(Original post by B_9710)
Yes.
awesome thanks
11. (Original post by Chittesh14)

Part (b)

I've come to so many equations and if I check the answer and sub he values, they all work. But, I can't get to the actual answer...

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Part a?
12. (Original post by B_9710)
Part a?
Part (b)
13. (Original post by timebent)
hmm i'll have a look tomorrow i think i know what you've done

awesome thanks
Okay :P.
14. (Original post by Chittesh14)
Part (b)
It's just simultaneous equations.
You have and .
It says that the modulus of is . So it's just Pythagoras. If you have a complex number then it's modulus is .
15. (Original post by B_9710)
It's just simultaneous equations.
You have and .
It says that the modulus of is . So it's just Pythagoras. If you have a complex number then it's modulus is .
I know, I did that 100 times. Idk why I'm getting it wrong. Maybe I got the values of z wrong (other way round).
16. (Original post by Chittesh14)
I know, I did that 100 times. Idk why I'm getting it wrong. Maybe I got the values of z wrong (other way round).
How about you take a picture of your workings and maybe we can see where you keep making the mistakes?
17. (Original post by Devify)
How about you take a picture of your workings and maybe we can see where you keep making the mistakes?
Yeah tomorrow, I'm too busy playing games.. lol.
I'll probably see my mistake tomorrow morning anyway somehow.
If not, I'll be mad and post it here, hoping for satisfaction.
18. (Original post by Chittesh14)

Part (b)

I've come to so many equations and if I check the answer and sub he values, they all work. But, I can't get to the actual answer...

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how does one do part A???
19. (Original post by timebent)
how does one do part A???
I'll explain that once I get out of bed lol

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20. (Original post by Chittesh14)
I'll explain that once I get out of bed lol

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how late u getting up xD

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