Year 12s: what will be the first way you research your future options? >>

'w-plane' questions

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:

Screen Shot 2016-04-18 at 20.18.52.png

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?

Reply 1

Zacken

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.

(edited 8 years ago)

Reply 2

B_9710

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