given the line $c$: $\Re(z)^2+\Im(z)^2=\arg(z),$
where $y$ is the imaginary part and $x$ is the real
$$$$i want to evaluate $$\int_C z^2\ dz, z=x+iy$$
so:
$$
\int_C z^2\ dz=\int_C\left(x+iy\right)^2\left(dx+idy\right){=\int_C\left[\left(x^2-y^2\right)dx-2xy\ dy\right]+i\int_C\left[2xy\ dx+\left(x^2-y^2\right)dy\right]}
$$im stack here, how can i continue?
Hint. Note that $$\int_{\gamma}z^2dz=\left[\frac{z^3}{3}\right]_{P}^Q$$ where $P$ is the starting point and $Q$ is the final point of the path $\gamma$.
P.S. BTW, what is the definition of $\arg(z)$? Is it the principal value with range $[0,2\pi)$?