Modulus and Argument of a complex number

 
Modulus:    It is defined as

                      \fn_cm |Z|=r=\sqrt{x^2+y^2}

Argument: Arg(Z):  It is defined as

                      \fn_cm \theta=tan^{-1}(\frac{y}{x})

it is also known as amplitude of Z    symbolically amp(Z)

Note:

  •  If |Z|=0 then x=0 and y=0
  • The Argument θ of a complex number is not unique.
  • If θ be the value of argument  so also is  2nπ + θ where n=0,± 1, ±2,…

 

 

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

                                                  \fn_cm -\pi < \theta \leqslant \pi

complex analysis mcqs

 

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