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Let z = x+iy denote the point P(x,y) in the xy plane.
Then from the figure, we have


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 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.

