# Polar expression of a complex number not centered at the origin.

I know that when we define $$z = re ^ {i theta}$$, for a complex number $$z = a + bi$$, and $$0 leq theta <2 pi$$say that $$theta$$ is the angle that the vector of origin, at the point $$(a, b)$$, made with the x axis. So for any curve around the origin, I can represent a point of the curve as $$z = r_ {1} e ^ {i theta_ {1}}$$.

My question is: how can I write a complex number in polar form, whose end of the vector does not originate? More specifically, on the photo I provided, how can I represent the vector whose tail is $$i$$ and the head is $$z$$, as a complex number in polar form?