Principal value of the argument of \cos 1200^{o}+i \sin 1200^{o} is:  

  • Option 1)

    300^{o}

  • Option 2)

    120^{o}

  • Option 3)

    -150^{o}

  • Option 4)

    180^{o}

 

Answers (1)

As learnt in concept

Definition of Argument/Amplitude of z in Complex Numbers -

\theta =tan^{-1}|\frac{y}{x}|, z\neq 0

\boldsymbol{\theta,\pi-\theta,-\pi+\theta,-\theta} are Principal Argument if z lies in first, second, third or fourth quadrant respectively.

- wherein

 

 tan\theta=\frac{sin 1200^{\circ}}{cos 1200^{\circ}} =  tan 1200^{\circ}

tan\theta=tan(1080^{\circ}+120^{\circ})

tan\theta=tan(120^{\circ})

\theta=120^{\circ}

 


Option 1)

300^{o}

This is incorrect option

Option 2)

120^{o}

This is correct option

Option 3)

-150^{o}

This is incorrect option

Option 4)

180^{o}

This is incorrect option

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