## Argand Diagrams

We can easily display complex numbers using an Argand diagram, very similarly to Cartesian coordinates.
Displaying the number
$z=x+ i y$
(where
$x, \: y$
are the real and imaginary components of
$z$
respectively, and
$i=\sqrt{-1}$
on an Argand diagram means plotting the point
$(x,y)$
and drawing a line from the origin to the point.

The magnitude of
$z$
is the length of the line so
$|z|= \sqrt{x^2+y^2}$
and the argument of
$z$
, written
$Arg(z)$
is the anfle
$\theta$
that
$z$
makes with the positive real (or
$x$
) axis. takien counter clockwise.
We can also write
$z= x+iy = \sqrt{x^2+y^2} e^{i tan^{-1}(y/x)}$