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

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