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Help me understand! - Complex numbers and quadratic equations - JEE Main-13

Principal argument of \sqrt{3}-i equals

  • Option 1)

    \frac{-\pi }{3}

  • Option 2)

    \frac{-\pi }{4}

  • Option 3)

    \frac{-\pi }{6}

  • Option 4)

    \frac{-\pi }{12}

 
Answers (1)
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\because \sqrt{3}-i lies in 4th quadrant

\therefore \Theta =\tan ^{-1}\left | \frac{-1}{\sqrt{3}} \right |=\frac{\pi }{6}

\therefore Principal argument = \frac{-\pi }{6}

\therefore Option (C)    

 

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

 

 


Option 1)

\frac{-\pi }{3}

This is incorrect

Option 2)

\frac{-\pi }{4}

This is incorrect

Option 3)

\frac{-\pi }{6}

This is correct

Option 4)

\frac{-\pi }{12}

This is incorrect

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