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Im having trouble with this question about complex mapping. Line $ y=2x-1$ (Where $ y=Im(z)$ and $ x=Re(z)$ ) is mapped in mapping $ z \mapsto z^2$ . Determine the equation of parabola of the image. What I have tried I started with $ w=f(z)=(x+iy)^2=x^2-y^2+2ixy=U(x,y)+iV(x,y)$ and since $ y=2x-1$ , $ \begin{cases} U_x=x^2-(2x-1)^2 &\ V_x=2x(2x-1)Read more