Complex Numbers


   
 
Polar form of a Complex number
 
 
Let z = x+iy denote the point P(x,y) in the xy plane.
 
 
Then from the figure, we have
 
 
 
 
 
z = r{cosq+isinq} is called the polar form of the complex number.
 
x + iy (which is in the cartesian form) where   is called the modulus of the complex number z denoted by |z| and q = tan-1 y/x is called the amplitude or argument of the complex number z denoted by amp(z) or arg(z).
 
The value of q is such that -p < q £  p, is called the principal value of the amplitude.
 
The general value of the amplitude is q + 2np, where n is positive or negative integer and is the principal value of the amplitude.
 
To find the principal value of (amplitude) from the equation cos q = x/r and sin q = y/r, the following table is useful.
 
 
 
     
   
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