Roots of Equations Further Maths Help

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.

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 ...)

Thanks
I got my final answer as z = 3 + 3/2 i

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

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

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.

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

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

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!

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!