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1. 1. For the transformation w = 1/z find the locus of w when:
b. z lies on the half line with equation arg z = pi/4
c. z lies on the line with equation y = 2x + 1

2a.
$cos^{2}(\frac{\pi}{10}) = \frac{5 + \sqrt{5}}{8}$

Using this write down the exact value of $cos^{2}(\frac{3\pi}{10})$

3. z = -9 + 3root(3)i |w| = root(3)

what is zw and z/w
2. (Original post by Carman3)
1. For the transformation w = 1/z find the locus of w when:
b. z lies on the half line with equation arg z = pi/4
c. z lies on the line with equation y = 2x + 1

2a.
$cos^{2}(\frac{\pi}{10}) = \frac{5 + \sqrt{5}}{8}$

Using this write down the exact value of $cos^{2}(\frac{3\pi}{10})$

3. z = -9 + 3root(3)i |w| = root(3)

what is zw and z/w
What have you done/tried and where are you stuck? Any working so far?
3. (Original post by ghostwalker)
What have you done/tried and where are you stuck? Any working so far?
Sorry i should mention i can now do the first one.
The second one not sure where to start tbh.
On the third one not sure what to do with the mod w so not sure where to start with that either
4. (Original post by Carman3)
Sorry i should mention i can now do the first one.
The second one not sure where to start tbh.
On the third one not sure what to do with the mod w so not sure where to start with that either
Hints:

For the second one, I'd start by looking how to express in terms of , then square the whole equation.
I could be missing a trick there, as it says "write down" which usually implies no working required, but if I am, I can't see it.

For the third one, converting everything into the form looks to be the easiest root.
5. (Original post by Carman3)
The second one not sure where to start tbh.
Are you sure you've written the full question down for Q2? It should normally be something about roots of a polynomial in cos or sin...
6. (Original post by Zacken)
Are you sure you've written the full question down for Q2? It should normally be something about roots of a polynomial in cos or sin...
The full question was show that ...... = the above equation and i could do that part but the second part of the equation was what i typed and couldnt do also didnt want to type whole question if its not necessary takes more effort
7. (Original post by Carman3)
The full question was show that ...... = the above equation and i could do that part but the second part of the equation was what i typed and couldnt do also didnt want to type whole question if its not necessary takes more effort
Right, but question parts are usually related (and it could be in this case). What was your working out for the first part? Did it have something to do with cos^2 (pi/10) being the root of a certain polynomial?
8. (Original post by Carman3)
...
I suspect Zacken's suspicions are correct. The question, as it stands, is very unusual, and I've not seen one like that at A-level before.

Updated: March 20, 2017
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