The absolute value of i, the imaginary sqrt
(-1), is 1. Let me demonstrate in a pitiful graph:
_ _ _ _ _ _|_ _ _ _ _ _
-3 -2 -1 | 1 2 3
This is a crummy model of the complex plane
, where the y axis has been replaced with i. The dynamics
of finding all absolute value
s 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 non-imaginary Real Numbers
) to 0 is it's absolute value. So the point x's absolute value, from above, is sqrt(2), because abs(a2
) + abs(b2
) = c2
, 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.