Show that the transformation w=z² is conformal at point z=1+i by finding the images of the lines y=x and x=1 which intersect at z=1+i. The question is:
Show that the transformation w=z² is conformal at point z=1+i by finding the images of the lines y=x and x=1 which intersect at z=1+i.
I am not sure how to proceed with this question. Please help.

Hint: An analytic function $f(z)$ is conformal at a point $z=a$ if $f'(a)$ is non-zero. The given function $f(z)=z^2$ is analytic and $f'(1+i)$=$2(1+i)$ which is non-zero.
