Further Pure Maths HELP

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13gpinsonbradley
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#1
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#1
I am really stuck on this question.... can someone help?

The complex number w satisfies |w-4i| = 3
Find the maximum value of arg w in the interval (-pi,pi)
Give your answer in radians correct to 2 decimal places
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Justvisited
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#2
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#2
Look at it on an Argand diagram, and realise that this locus is a circle centre (0, 4) and radius 3.

So basically it's asking for the argument of the point where a line going through the origin is tangent to the circle on its left side.

Can you do this? Should be GCSE level maths now.
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Justvisited
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#3
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#3
Let me know if you're still stuck.
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Justvisited
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#4
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#4
So you already know that the coordinates of the point we're looking for satisfy the equation of the circle I described, viz.

x² + (y - 4)² = 3²

Now you need to derive another equation from the constraints imposed by the definition of what we're looking for. I definitely think a geometric/visualising approach is the easiest.
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Justvisited
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#5
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#5
Next hint: since the tangent is perpendicular to the radius where they meet at the point of interest, we have a right angled triangle whose hypotenuse lies on the y axis. You can use one of the GCSE circle theorems to realise that the hypotenuse is therefore the diameter of a circle whose circumference contains the POI, and use this fact to derive another circle equation safisfied by the coordinates of the POI.
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Justvisited
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#6
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#6
Do you see that the other two corners of this triangle are the origin and the centre of the first circle, at (0, 4)?
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RDKGames
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#7
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#7
(Original post by Justvisited)
Do you see that the other two corners of this triangle are the origin and the centre of the first circle, at (0, 4)?
Might want to wait for OP to reply first ?
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Justvisited
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#8
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#8
(Original post by RDKGames)
Might want to wait for OP to reply first ?
I did. See times of posts above. It's very strange they haven't bothered to check their own thread for answers. Shall we lock it?
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RDKGames
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#9
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#9
(Original post by Justvisited)
I did. See times of posts above. It's very strange they haven't bothered to check their own thread for answers. Shall we lock it?
No need to lock the thread.

Your first (or any subsequent) post might've been sufficient and OP already has the answer without replying -- no point posting more tips if OP doesn't respond.
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Justvisited
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#10
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#10
(Original post by RDKGames)
No need to lock the thread.

Your first (or any subsequent) post might've been sufficient and OP already has the answer without replying -- no point posting more tips if OP doesn't respond.
Yeah. But if OP already has the answer and method there was no point in their posting!!
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RDKGames
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#11
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#11
(Original post by Justvisited)
Yeah. But if OP already has the answer and method there was no point in their posting!!
Not sure what you mean. Nothing here suggests they had the answer and method before posting.

The scenario is quite common; OP gets a question, doesn't know how to do it, asks on here, gets a reply with a hint, OP solves it without responding to the poster and moves on.
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Justvisited
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#12
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#12
(Original post by RDKGames)
Not sure what you mean. Nothing here suggests they had the answer and method before posting.

The scenario is quite common; OP gets a question, doesn't know how to do it, asks on here, gets a reply with a hint, OP solves it without responding to the poster and moves on.
If they were utterly stuck with it to start with, I somehow doubt whether my initial response by itself would have been enough to unlock it for them.

Meanwhile, having seen quite a few of these maths threads, I don't recall any where the OP never returned after opening it, so I'm surprised that you're claiming this is common.
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RDKGames
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#13
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#13
(Original post by Justvisited)
If they were utterly stuck with it to start with, I somehow doubt whether my initial response by itself would have been enough to unlock it for them.

Meanwhile, having seen quite a few of these maths threads, I don't recall any where the OP never returned after opening it, so I'm surprised that you're claiming this is common.
Having replied to thousands of these threads, it does tend to happen, so I wouldn't waste my energy replying to a possibly already dead thread until OP replies. But you do you.
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13gpinsonbradley
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#14
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#14
Thank you. I got this far.
Sorry for the late response
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Notnek
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#15
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#15
(Original post by GBP23)
Thank you. I got this far.
Sorry for the late response
Are you saying you're still stuck? If you are, please post all your working.
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Notnek
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#16
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#16
(Original post by RDKGames)
Having replied to thousands of these threads, it does tend to happen
You're ahead in the race to 15,000 but there's still time for me...
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RDKGames
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#17
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#17
(Original post by Notnek)
You're ahead in the race to 15,000 but there's still time for me...
Is there a prize at 15,000 ?
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Notnek
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#18
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#18
(Original post by RDKGames)
Is there a prize at 15,000 ?
There better be otherwise the last 13 years have been a waste for me.
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Justvisited
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#19
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#19
(Original post by Notnek)
Are you saying you're still stuck? If you are, please post all your working.
She PMed me to say she got there eventually, but who knows?
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