The absolute value of i, the imaginary
sqrt(1), is 1. Let me demonstrate in a pitiful graph:
X 3i

2i

1i x
_ _ _ _ _ __ _ _ _ _ _
3 2 1  1 2 3
1i

2i

3i

This is a crummy model of the
complex plane, where the y axis has been replaced with i. The
dynamics of finding all
absolute values from here on should be familiar.
One is 1 unit away from
zero (making 1 it's absolute value), and so are 1, i, and i. To get a little more advanced with the concept, let me show how such knowledge can be applied. The
distance from any
complex number (including the set of nonimaginary
Real Numbers) to 0 is it's absolute value. So the point x's absolute value, from above, is sqrt(2), because abs(a
^{2}) + abs(b
^{2}) = c
^{2}, where c is the distance or absolute value (thank you,
Pythagoras). Sqrt(1 + 1) = sqrt(2), so we can divine that the complex number...
(1 + i)
^ ^
a + b
...has an absolute value of sqrt(2). Like wise, X has a complex value of (2 + 3i), and an absolute value of sqrt(15). Any of the concepts that one has learned in
algebra regarding simple 2d line segments applies, but once one steps much further the nasty fact that i = sqrt(1) kicks in, so the traditional concept of
function based graphical algebra kind of gets thrown out the window.