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    (Original post by A Slice of Pi)
    The 'slim bits' are from the loop of the second curve. Work out the polar coordinates of where the curves meet first, and then use integration to find the area of one of these bits (e.g. take the smaller of the two angles from part (a) and 0 as the limits). By symmetry you only need to work out the area of one of the two slim pieces and then just double the answer, then add it on to the area of the sector.
    Got it, thank you!
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    I thought some of you might like to have a go at this exam-style question I put together on complex numbers for a bit of extra practice. It seems to be a tough topic on these FP2 papers
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    (Original post by A Slice of Pi)
    I thought some of you might like to have a go at this exam-style question I put together on complex numbers for a bit of extra practice. It seems to be a tough topic on these FP2 papers
    This is my answer for the second part:
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    (Original post by coolguy123456)
    This is my answer for the second part:
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    Correct
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    (Original post by A Slice of Pi)
    I thought some of you might like to have a go at this exam-style question I put together on complex numbers for a bit of extra practice. It seems to be a tough topic on these FP2 papers
    For part b) , I got 5/(5-3sqrt2) as my answer, which is 6.6. Have I done it wrong? If so, how would you do it? Cheers
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    Question: If you are given 2 equations and 2 curve on the graph, without any label , how do you know which one is which ?? for example this one,i could do it because i know root3 sin theta is the circle, but in the worst case where i have no idea which one to integrate, what would i do ???
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    (Original post by tripleseven)
    For part b) , I got 5/(5-3sqrt2) as my answer, which is 6.6. Have I done it wrong? If so, how would you do it? Cheers
    I'll post my working to the question later if that helps.


    (Original post by anndz3007)
    Name:  Screen Shot 2016-05-26 at 18.14.00.png
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    Question: If you are given 2 equations and 2 curve on the graph, without any label , how do you know which one is which ?? for example this one,i could do it because i know root3 sin theta is the circle, but in the worst case where i have no idea which one to integrate, what would i do ???
    The clue is in the diagram with this one. When the angle theta is zero, one of those curves is at the origin and one is not. Putting theta = zero into each of the two equations should reveal which is which.
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    (Original post by A Slice of Pi)
    I thought some of you might like to have a go at this exam-style question I put together on complex numbers for a bit of extra practice. It seems to be a tough topic on these FP2 papers
    Here's my solution...
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    (Original post by Music With Rocks)
    Would you ever be asked to prove  z=re^i ^\theta ?
    I think you could be asked to prove it by induction, but I cant find a solution. This is one with reference to series expansions.

    

e^x = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \frac{x^4}{4!} + ... + \frac{x^n}{n!}



x = i\theta



e^i^\theta = 1 + i\theta + \frac{(i\theta)^2}{2!} + \frac{(i\theta)^3}{3!} + ... + \frac{(i\theta)^n}{n!}



e^i^\theta = 1 +i\theta + \frac{i^2 \theta^2}{2!} + \frac{i^3 \theta^3}{3!} + ... + \frac{i^n \theta^n}{n!}



e^i^\theta = 1 +i\theta - \frac{\theta^2}{2!} - \frac{i \theta^3}{3!} + \frac{\theta^4}{4!} + ...



e^i^\theta = (1 - \frac{\theta^2}{2!} + \frac{\theta^4}{4!} + ...) + i(\theta - \frac{\theta^3}{3!} + \frac{\theta^5}{5!} + ...)



(Using expansions for \cos\theta, \sin\theta)



e^i^\theta = \cos\theta + i\sin\theta



If z = r(\cos\theta + i\sin\theta), z = re^i^\theta
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    Zacken question regarding inequaltiies in FP2. So if we have a question such as the one attached how would i know which inequality to use namely greater than as opposed to greater than or equal to. ( I know when the question has an inequality with strictly i write my answers with ONLY strictly but when the question shows not strictly I'm never sure which inequality to use in my answer)
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    Is proof by induction part of fp2? has it come up in an exam b4?
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    (Original post by ChuckNorriss)
    Is proof by induction part of fp2? has it come up in an exam b4?
    June 2013 Q4a, proof by induction of de moivres.
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    (Original post by Davidabraham)
    Zacken question regarding inequaltiies in FP2. So if we have a question such as the one attached how would i know which inequality to use namely greater than as opposed to greater than or equal to. ( I know when the question has an inequality with strictly i write my answers with ONLY strictly but when the question shows not strictly I'm never sure which inequality to use in my answer)
    Do you mean that the answer(s) include a mixture of greater than and greater than or equal to? The way I would approach this is to consider how the signs of the expressions change in the different regions x > 2, x = 2, 0 < x < 2, x = 0, -3 < x < 0, x = -3, x < -3. Now, for the functions to be defined, we cannot have x = 2 or 0, so we discard these and focus on the other regions. The mixture of greater than and greater than or equal to is from the fact that some of the ranges of values obtained by solving the equation in each region may not coincide with the region that is being considered.
    For example: if you solve the inequality in the case 0 < x < 2, you get the solution as -2 <= x <= 1.5. We choose a stricter range of values that agrees with both inequalities, i.e. 0 < x <= 1.5.
    Hope some of that helps, feel as though I was explaining it badly.
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    Please could someone explain question 9b on here, really can't figure it out! Thanks Name:  image.jpg
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    (Original post by economicss)
    Please could someone explain question 9b on here, really can't figure it out! Thanks Name:  image.jpg
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    Work out the area of the triangle between OA and the line theta=pi/2. You would then use polar coordinate integration of the curve between the value of theta you got for the coordinates of A (from part a) and pi/2, then subtract this from the area of the triangle.
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    (Original post by economicss)
    Please could someone explain question 9b on here, really can't figure it out! Thanks Name:  image.jpg
Views: 134
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    Try find the area of the triangle from OA(to the pi/2 line).

    Then integrate from A to the initial line to find the remaining area.

    Then add the two areas? Try that and let me know if it works :P

    Whoops misread the Q thought it was finding the total area!
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    (Original post by Davidabraham)
    Zacken question regarding inequaltiies in FP2. So if we have a question such as the one attached how would i know which inequality to use namely greater than as opposed to greater than or equal to. ( I know when the question has an inequality with strictly i write my answers with ONLY strictly but when the question shows not strictly I'm never sure which inequality to use in my answer)
    A good way to be sure is if you have a < x < b as a solution and you're not sure whether those inequalities should be strict or not, plug a and b into the inequality, if the inequality is still true then it's non-strict.
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    (Original post by economicss)
    Please could someone explain question 9b on here, really can't figure it out! Thanks Name:  image.jpg
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    Hi, what book is that from?
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    Hello, I don't understand the answer to this question. The answer is r=(2/9)root6cosectheta but I don't understand why you need the cosectheta bit since you know what sintheta is. Couldn't you just sub that in and get r=some constant? Because there's only one point where the line is parallel to the initial line.
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    (Original post by target21859)
    Hello, I don't understand the answer to this question. The answer is r=(2/9)root6cosectheta but I don't understand why you need the cosectheta bit since you know what sintheta is. Couldn't you just sub that in and get r=some constant? Because there's only one point where the line is parallel to the initial line.
    The final answer is describing the equation of the line. The value of sin theta found in the first few lines is for where the line meets the curve. Points on the actual line have different values of r and theta, so you can't say that theta is constant.
 
 
 
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