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    I'm struggling with the following FP2 Q6 from Jun 09.
    A Transformation T from the z-plane to the w-plane is given by w=z/z+i.
    The circle with equation (mod z)=3 s mapped by T onto the curve C
    Show that the curve is a circle and give it's radius.
    I have found z in terms of w. But have a term which is wi and I'm not sure how to put that into Cartesian form. I have tried wi=ui-v but that has given me a slightly incorrect answer.
    Help would be greatly appreciated =)
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    (Original post by EduinJBL)
    I'm struggling with the following FP2 Q6 from Jun 09.
    A Transformation T from the z-plane to the w-plane is given by w=z/z+i.
    The circle with equation (mod z)=3 s mapped by T onto the curve C
    Show that the curve is a circle and give it's radius.
    I have found z in terms of w. But have a term which is wi and I'm not sure how to put that into Cartesian form. I have tried wi=ui-v but that has given me a slightly incorrect answer.
    Help would be greatly appreciated =)
    rearrange to get z in terms of w like you have already done, then use  |z| = 3 to get 3 in terms of w, then multiply out the bottom and use  w = u + iv

    Edit:  |iw| = 1|w| that's the bit you needed isn't it, sorry I forgot that
    because  |iw|  = |ui - v| = u^2 + v^2 = |w|
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    Thanks alot, that makes perfect sense and gives me the correct answer.
 
 
 
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