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# 'w-plane' questions

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1. 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:

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?
2. (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 given by , input it into your transformation and get it in the form then show that satisfies the given locus since it lies on the real axis, we have that .

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.
3. 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 .
I would find w in terms of x and y, and then equate the imaginary part to 0.

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