Parametric form of curve $\vert z+i\vert = 1$

Question

I need to integrate a complex function through the curve $\vert z+i\vert = 1$. As far as I know I need the parametric form of this curve. I know that when I have $\vert z\vert = 1$, the parametric form is something like $\cos(t) + i\sin(t)$. But what's different when I have that "$+i$"?

Answer 1

$$ |z-z_0| = r $$ is the equation of a circle centered in $z_0$ with radius r. Its parametric form is $$ z = z_0 + re^{it} = z_0 + r(\cos t + i \sin t) $$