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'w-plane' questions

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Why bother with a post grad? Are they even worth it? Have your say! 26-10-2016
    • Thread Starter

    Could someone explain to me what I am generally supposed to do in these sorts of questions, I thought I knew them from doing the exercises but in actual papers these really confuse me.

    For example:

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    5 a) and b) were no problem whatsoever, but I have no clue what do for part c).

    I started off by making z the subject, but I really don't know what to do. Is there a general kind of thing I am supposed to be aiming for with this type of question?

    (Original post by 雷尼克)
    I started off by making z the subject, but I really don't know what to do. Is there a general kind of thing I am supposed to be aiming for with this type of question?
    There are two ways to do this. The usual way is to take a general points Q given by x + iy, input it into your transformation and get it in the form w = \Re(w) + i\Im(w) then show that \Im(w) satisfies the given locus since it lies on the real axis, we have that \Im(w) = 0.

    The second way is the nicer way and involves thinking about the real axis as a perpendicular bisection. I'll leave you to figure that one out for yourself.

    Notice that Q is mapped from the z-plane to R in w-plane, rather than the other way round as it can be in some questions. The point R lies on the imaginary axis so  \Im(w) = 0 .
    I would find w in terms of x and y, and then equate the imaginary part to 0.
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