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?