Argument of a complex number:

Let  z = x + iy be a complex number then its magnitude is described by the real number √x²+y² and is shown by |z|. 

If z = x + iy then angle q provided by tanθ =y/x  is called to be the argument or amplitude of the complex number z and is shown by arg (z) or amp (z). In that case of x = 0 (where y ≠ 0), arg (z)  = + Π/2 or -Π/2 relaying on upon y > 0 or y < 0 and the  complex  number is known as completely  imaginary. If y = 0 (where x¹0), then arg (z) = 0 or p relaying upon x > 0 or x < 0 and the complex number is known as completely real. The argument of the complex number 0 is not described.

We may describe the argument of a complex number also as any number of the θ which assures the system of equations . 

Principal argument of a complex number:

The value of q fulfilling the inequality - Π < θ ≤ Π is known as the principal value of the argument.

 Method of searching the principle argument of a complex number z = x + iy

Example:      For z =  √3 - i, calculate  the  principal value  of  arg(z).

 Solution:     

            => Principal value of arg z = -Π/6.    (Since z present in the fourth quadrant)

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