I am attempting to determine the locus of z for $\mathrm{arg}({z}^{2}+1)$. I do know that since ${z}^{2}+1=(z+i)(z-i)$, I could write $\mathrm{arg}({z}^{2}+1)=\mathrm{arg}(z+i)+\mathrm{arg}(z-i)$ but I don’t really know how to figure out the locus of the points from here. How should I approach this? Is there a relationship with the difference in two arguments (arc of a circle)? Thank you!