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    (Original post by TheBBT)
    Quick question: When plotting points on an Argand diagram do you have to draw lines to the point from the origin? This is usually when plotting the roots of a complex number.
    Don't think so, but if you have space perhaps label the points?

    Like z = 1 + j

    I don't think either of these are required though, unless asked or implied.
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    This is very confusing. When its to do with eigen vectors and M. I know Mx=Yx ... but this makes no sense. M^2v and M^-1v ??
    Someone please help. What even is M in these equations?

    Jan 2012 Q3, eigen vector is displayed in answers and lambda =5

    Do you replace M with lambda ??
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    (Original post by HFancy1997)
    So worried about this exam, need an A for this...any predictions?

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    I predict questions on Polar Coordinates, Matrices, Complex Numbers and Hyperbolic functions.
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    (Original post by Wunderbarr)
    Don't think so, but if you have space perhaps label the points?

    Like z = 1 + j

    I don't think either of these are required though, unless asked or implied.
    thank you! I was never sure because some mark schemes have them and others don't, and I don't really see what the point of them is
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    (Original post by Wunderbarr)
    I predict questions on Polar Coordinates, Matrices, Complex Numbers and Hyperbolic functions.
    I hope they come up too, ive prepared for those

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    (Original post by TheBBT)
    thank you! I was never sure because some mark schemes have them and others don't, and I don't really see what the point of them is
    If you draw the lines, it can be used to explain why the w3 +w2 + w = 0 thing is true, by looking at the vector sum of the lines (if drawn as vectors going from the origin to Z).
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    (Original post by Bealzibub)
    Do you replace M with lambda ??
    My Matrices knowledge isn't the best, but I believe Mv = \lambda v

    So yes, perhaps treat M as lambda since it is suggested M = \lambda for an eigenvector v.
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    Does anyone know the polar graphs we're expected to remember? Specifically for those 2 markers?
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    (Original post by Wunderbarr)
    Does anyone know the polar graphs we're expected to remember? Specifically for those 2 markers?
    You have to remember some??? Oh god, I hope not... ive just been plotting them for coordinates I get from my calculator

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    (Original post by HFancy1997)
    You have to remember some??? Oh god, I hope not... ive just been plotting them for coordinates I get from my calculator

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    Well it's a lot quicker to remember the ones they may expect us to remember >_< .
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    Can anyone help me with this:

    ii) show that there is no positive integer n for which zn is imaginary.





    In the mark scheme, I don't understand where kpi comes from?
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    (Original post by Wunderbarr)
    Does anyone know the polar graphs we're expected to remember? Specifically for those 2 markers?
    Nah, I just use table functino on calculation so I can plot the graph
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    (Original post by Bealzibub)
    Nah, I just use table functino on calculation so I can plot the graph
    Fair, fair.
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    (Original post by HFancy1997)
    You have to remember some??? Oh god, I hope not... ive just been plotting them for coordinates I get from my calculatorPosted from TSR Mobile
    (Original post by Wunderbarr)
    Well it's a lot quicker to remember the ones they may expect us to remember >_< .
    (Original post by Bealzibub)
    Nah, I just use table functino on calculation so I can plot the graph
    Doesn't anyone else here use a graphic calculator?
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    (Original post by MintyMilk)
    Doesn't anyone else here use a graphic calculator?
    Graphical calc? whats that?

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    (Original post by MintyMilk)
    Doesn't anyone else here use a graphic calculator?
    No need for it at all, if you have decent casio calculator press MODE then 7 and you can use table mode, input a function specify a range for x values etc and it plots in a table for you. Then you can just plot the graph besides at most they are 2 mark questions anyway
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    (Original post by Bealzibub)
    No need for it at all, if you have decent casio calculator press MODE then 7 and you can use table mode, input a function specify a range for x values etc and it plots in a table for you. Then you can just plot the graph besides at most they are 2 mark questions anyway
    Yeah I know that, I used a standard casio to do that for my AS exams. I still use that calc for exact values, but the Ti-84 Plus CE just opens up so many more possibilities with checking answers etc. It's also just nicer to use than any scientific calc
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    (Original post by Bealzibub)
    Can anyone help me with this:

    ii) show that there is no positive integer n for which zn is imaginary.





    In the mark scheme, I don't understand where kpi comes from?
    Its imaginary if it's on the imaginary axis and so would have argument pi/2 or 3pi/2 the kpi bit just shows that you can add any multiple of pi and still be on the imaginary axis. It's like when you find roots of trig equations, there are infinitely many values if you just keep adding multiples of pi on etc.
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    (Original post by Bruhh)
    Its imaginary if it's on the imaginary axis and so would have argument pi/2 or 3pi/2 the kpi bit just shows that you can add any multiple of pi and still be on the imaginary axis. It's like when you find roots of trig equations, there are infinitely many values if you just keep adding multiples of pi on etc.

    Do you understand this? If so could you please explain how to do ii) or anyone else for that matter. Here are my thoughts: since its centered at origin, the middle vertex must be touching the y axis somewhere. If one of the vertex is in 1st quadrant then I'm imagining a triangle like this (upside down):
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    (Original post by Bealzibub)

    Do you understand this? If so could you please explain how to do ii) or anyone else for that matter. Here are my thoughts: since its centered at origin, the middle vertex must be touching the y axis somewhere. If one of the vertex is in 1st quadrant then I'm imagining a triangle like this (upside down):
    Since it's an equilateral triangle and you know one of the points, the other two can be found by rotating that point by 2pi/3 radians both clockwise and anticlockwise. So to find the other two points you'd multiply 2+4j by e^2jpi/3 and e^-2jpi/3. Then once you have those two points, you can use 1/2basexheight to work out the area.
 
 
 
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