Does a purely imaginary number have a corresponding "angle" in polar coordinate system?

Let's say we have a pure imaginary number with no real part, $i$.

I know that complex numbers in the form $a+bi$ can be converted into the polar coordinate system using the following relations:

1. $\theta = \arctan{Im/Re} $


2. $r = \sqrt{a^2+b^2} $

However, for a purely imaginary $i$ number with no real part, relation $1$ gives:

$$\theta = \arctan{1/0} $$

which is division by zero?