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# FP2 Complex Numbers Transformations (need help) watch

1. 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

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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2. (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.
3. (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
4. (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.
5. (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

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.
6. 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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