Consider the transformation

z $\displaystyle \mapsto$ w = −$\displaystyle 5z^2+3$ .

(a) Find the image of the line $\displaystyle Re(z) = c$ (for c a non-zero real constant) under the

transformation, using as usual $\displaystyle z = x + iy$ and $\displaystyle w = u + iv$.

(b) Find the equation of the line $\displaystyle Im(z) = k$ (for k a real constant).

Help please explain how to solve this.