Converting $i$ to exponential form

Question

How would I convert the irrational number $'i'$ to exponential form, or $e^{i\theta}$?

I'm working a little in De Moivre's theorem.

Answer 1

As you've already shown the effort in the comments and found the solution yourself, I'll use the answer box to post a picture and elaborate a little:

The argument, the angle of the rotation between the $\mathbb{R}^2$-vector(associated with the complex number) is thus simply a $\pi/2$(or $90^\circ$) turn. As you've said yourself, the coefficient $r$ of the representation of a complex number using the complex exponential is the associated magnitude, i.e.

$$|i|=|0+1\cdot i|=\sqrt{0^2+1^2}=1$$

Attribute for the picture: By Original: GuntherDerivative work: Wereon - This file was derived from: Euler's formula.png:, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=821342