Roots of Equations Further Maths Help

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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Reply 1

mqb2766

Original post by 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

Could you make The question a bit larger/clearer pls.

Reply 2

wbanner2001

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

Reply 3

mqb2766

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 ...)

Reply 4

wbanner2001

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

Reply 5

mqb2766

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?

Reply 6

wbanner2001

Original post by mqb2766

Presume you've checked by subbing it back into the equation?

Yeah - all good :smile:

Reply 7

wbanner2001

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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Reply 8

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.

Reply 9

wbanner2001

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 :smile:

Reply 10

wbanner2001

Sorry to bother you again but am I doing the right thing here needing to find the tangent:

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Reply 11

mqb2766

What are you doing, also what is the first part of the question?

Reply 12

wbanner2001

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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Reply 13

mqb2766

Write both equations as
a = ...
Then equate and solve.

Reply 14

wbanner2001

I did that originally - I just made an arithmetic error putting k=2 not 1/2 aha! Thanks for your help!

Reply 15

rrrjjfg

I'm a year late but do you know what paper this is from?

Reply 16

LVSDH

Original post by rrrjjfg

I'm a year late but do you know what paper this is from?

Thats what i want to know

Reply 17

rrrjjfg

Original post by wbanner2001

Attachment not found

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!

Reply 18

wbanner2001

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!