Modulus and Argument of a complex number

Modulus:    It is defined as

$\fn_cm&space;|Z|=r=\sqrt{x^2+y^2}$

Argument: Arg(Z):  It is defined as

$\fn_cm&space;\theta=tan^{-1}(\frac{y}{x})$

Note:

Principal Value Argument.:   The value of argument which satisfy the inequality

$\fn_cm&space;-\pi&space;<&space;\theta&space;\leqslant&space;\pi$

complex analysis mcqs