Complex Transformations

Hi,

I'm really confused with complex transformations and how they work. I have learnt the method, but I really don't understand any of the theory behind it - I don't really know why I'm doing what I am doing.

When given a transformation T from the z-plane to the w-plane, and we have to find the locus of a point in the w-plane, why do we have to make z the subject of our transformation? What is the purpose of that?

Maybe if someone could explain what exactly each step of the calculation is doing in 'transforming' the point, I might understand what I'm doing. At the moment, I have no confidence in my technique...

Question 5(c) is an example where I have absolutely no idea what I am doing, despite getting the correct answer:

https://8dedc505ac3fba908c50836f59059ccce5cd0f1e.googledrive.com/host/0B1ZiqBksUHNYdHIxUkJmdndfMlE/June%202011%20QP%20-%20FP2%20Edexcel.pdf

Hi,

I'm really confused with complex transformations and how they work. I have learnt the method, but I really don't understand any of the theory behind it - I don't really know why I'm doing what I am doing.

When given a transformation T from the z-plane to the w-plane, and we have to find the locus of a point in the w-plane, why do we have to make z the subject of our transformation? What is the purpose of that?

Maybe if someone could explain what exactly each step of the calculation is doing in 'transforming' the point, I might understand what I'm doing. At the moment, I have no confidence in my technique...

Question 5(c) is an example where I have absolutely no idea what I am doing, despite getting the correct answer:

https://8dedc505ac3fba908c50836f59059ccce5cd0f1e.googledrive.com/host/0B1ZiqBksUHNYdHIxUkJmdndfMlE/June%202011%20QP%20-%20FP2%20Edexcel.pdf

Start off by writing w in terms of z. Then multiply and divide by the complex conjugate of the denominator of w which is 3-iz. When you write z=x+iy you should get the catesian equation you got in part b. This shows that z lies on C.