Roots of Equations Further Maths Help

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wbanner2001
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I need to use the fact that it has exactly one root to find the y part - do I use the quadratic formula on the last bit I have written?

I have x already and z = x+iy
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mqb2766
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(Original post by wbanner2001)
Attachment 888836

I need to use the fact that it has exactly one root to find the y part - do I use the quadratic formula on the last bit I have written?

I have x already and z = x+iy
Could you make The question a bit larger/clearer pls.
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wbanner2001
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(Original post by mqb2766)
Could you make The question a bit larger/clearer pls.
zz* + 3iz = p + 9i
where z is a complex number and p is a real constant.
Given that this equation has exactly one root, determine the complex number z
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mqb2766
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(Original post by wbanner2001)
zz* + 3iz = p + 9i
where z is a complex number and p is a real constant.
Given that this equation has exactly one root, determine the complex number z
Not checked your working but if there is only one solution, your quadratic in y must have a single soln, so discriminant is zero or complete the square (same thing ...)
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wbanner2001
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(Original post by mqb2766)
Not checked your working but if there is only one solution, your quadratic in y must have a single soln, so discriminant is zero or complete the square (same thing ...)
Thanks
I got my final answer as z = 3 + 3/2 i
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mqb2766
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(Original post by wbanner2001)
Thanks
I got my final answer as z = 3 + 3/2 i
Presume you've checked by subbing it back into the equation?
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wbanner2001
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(Original post by mqb2766)
Presume you've checked by subbing it back into the equation?
Yeah - all good
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wbanner2001
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(Original post by mqb2766)
Presume you've checked by subbing it back into the equation?
Could you check where I have gone wrong on this proof by induction stage 3:

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mqb2766
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When you add the k+1^th term, you multiply by 3/3 to get a 1/3 outside the factors. However only one of the factors should be multiplied by 3. If you multiply them both you're doing 9/3.
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wbanner2001
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(Original post by mqb2766)
When you add the k+1^th term, you multiply by 3/3 to get a 1/3 outside the factors. However only one of the factors should be multiplied by 3. If you multiply them both you're doing 9/3.
Ah fab! Done it now
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wbanner2001
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Sorry to bother you again but am I doing the right thing here needing to find the tangent:


[attach]888918[/attachm]
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mqb2766
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What are you doing, also what is the first part of the question?
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wbanner2001
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(Original post by mqb2766)
What are you doing, also what is the first part of the question?
Completed that but I can’t work out why my values for a here are inconsistent:

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mqb2766
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Write both equations as
a = ...
Then equate and solve.
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wbanner2001
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I did that originally - I just made an arithmetic error putting k=2 not 1/2 aha! Thanks for your help!
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rrrjjfg
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I'm a year late but do you know what paper this is from?
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LVSDH
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(Original post by rrrjjfg)
I'm a year late but do you know what paper this is from?
Thats what i want to know
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rrrjjfg
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(Original post by wbanner2001)
Attachment 888836

I need to use the fact that it has exactly one root to find the y part - do I use the quadratic formula on the last bit I have written?

I have x already and z = x+iy
If you still remember what paper this is, please let us know!
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wbanner2001
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(Original post by rrrjjfg)
If you still remember what paper this is, please let us know!
Hi, I left school late year but I am pretty sure they are Edexcel restricted access ones for teachers only - so unfortunately for you there won’t be a mark scheme available. Sorry I can’t help further but best of luck with your exams!
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rrrjjfg
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(Original post by wbanner2001)
Hi, I left school late year but I am pretty sure they are Edexcel restricted access ones for teachers only - so unfortunately for you there won’t be a mark scheme available. Sorry I can’t help further but best of luck with your exams!
Ah, that makes sense. Thank you anyway!
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