Transformations from the z-plane to the w-planeEdexcel International A Level Further Maths: Mind map

Exam questions on Transformations from the z-plane to the w-plane

1. The transformation $T$ from the $z$-plane to the $w$-plane is given by $w=z^2$, where $z=x+iy$ and $w=u+iv$.
   Find a Cartesian equation for the image of the line $x=2$ under $T$.2 marks
2. The transformation $T$ from the $z$-plane to the $w$-plane is given by $w=(1+i)z-2$.
   The circle $|z|=1$ is mapped by $T$ to a circle in the $w$-plane. Find its centre and radius.2 marks
3. The transformation $T$ from the $z$-plane to the $w$-plane is given by $w=\frac{z+i}{z-i}$, $z\neq i$, where $z=x+iy$ and $w=u+iv$.
   Show that the image of the real axis ($y=0$) lies on the circle $|w|=1$.3 marks