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    I attempted this question but I don't think I was on the right track.

    The transformation T from Z plane to W plane is given by

                w=\frac{Z+2}{Z+i}

    Show that the image,under T, of the imaginary axis in the z-plane is a line L in the w-plane. Find the equation of L.

    This is how I started:


    Then compare the coefficients? It looks long so I dont know if im doing it right
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    (Original post by bigboateng)
    Show that the image,under T, of the imaginary axis is in the Z plane. Find the equation of L.
    Perhaps I'm being thick, but I can't make sense of that statement.

    If you mean the imaginatry axis in the z plane, then I'd let z=ai, and plug it into your transformation and simplify, rather than try to use the reverse transformation.
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    (Original post by ghostwalker)
    Perhaps I'm being thick, but I can't make sense of that statement.

    If you mean the imaginatry axis in the z plane, then I'd let z=ai, and plug it into your transformation and simplify, rather than try to use the reverse transformation.
    haha yeah I was falling asleep whiles typing it, Ive editted it. & I just realised that its talking about just the imaginary line
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    (Original post by bigboateng)
    haha yeah I was falling asleep whiles typing it, Ive editted it. & I just realised that its talking about just the imaginary line
    Cool. If you follow my previous suggestion, it should come out easily.
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    (Original post by bigboateng)
    I attempted this question but I don't think I was on the right track.

    The transformation T from Z plane to W plane is given by

                w=\frac{Z+2}{Z+i}

    Show that the image,under T, of the imaginary axis in the z-plane is a line L in the w-plane. Find the equation of L.

    This is how I started:


    Then compare the coefficients? It looks long so I dont know if im doing it right
    the solution to your problem is 2 lines from where you have reached (assuming your are correct up to that point)

    Looking at your workings ... Having solved for z correctly.

    If you map the imaginary axis in the z plane, that means Rez = 0 ...

    ...which in turn it means the numerator of your "real part" is zero which gives the line instantly on simplification.

    The alternative which is to leave it as w=F(z) and sub z=ti also works but this will lead to parametrics. The parametrics here are not bad (I hope you solved it) but sometimes they are horendous

    I am sure you have solved for z (which is unituitive) for a reason (I suspect your teacher told or your book suggests to do so.

    In this type of questions I would also suggests that solving for z usually, but not always,works better.
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    A bit random but would anyone say dropping M1 for FP2 is stupid as I dislike Mechanics?Also pure modules are helpful for someone like me as Im doing Economics and a lot of Further methods are used I believe whereas I would almost never use any M1 methods in econ.
 
 
 
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