Let $T(z)=1/z$. Find the image of $y=2x+1$ under $T$.
I assume x and y are the real and imaginary part of z.
Basically what I need was let $w=1/(x+(2x+1)i)$ then multiplied by the complex conjugate we have that the real imaginary part of x.
Then should we equate coefficient with the equation of a circle? I dont know how to proceed.
From university, I know that the image must be a circle or a line since the transformation is a Mobius transformation. How is an A level student meant to get this?
i just looked at another question. Do i need to find two points such that this line is the locus for those two points? Then i sub that in?