Argand Diagrams

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

argand diagram

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

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