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  • I need help with - Complex numbers and quadratic equations - JEE Main-9

Let z_{1} & z_{2} are two complex numbers such that \bar{z_{1}}-\bar{z_{2}}= \sqrt{3}+i then arg \left ( z_{1}-z_{2} \right )  equals

  • Option 1)

    \frac{-\pi }{6}

  • Option 2)

    \frac{-\pi }{4}

  • Option 3)

    \frac{\pi }{4}

  • Option 4)

    \frac{\pi }{3}

 

Answers (1)

best_answer

\bar{z_{1}}-\bar{z_{2}}= \sqrt{3}+i

\Rightarrow \overline{z_{1}-z_{2}}= \sqrt{3}+i\Rightarrow z_{1}- z_{2} = \sqrt{3}-i

\because z_{1}-z_{2} lies in the fourth quadrant 

so arg \left ( z_{1}-z_{2} \right )= -\tan ^{-1}\left | \frac{-1}{\sqrt{3}} \right |= \frac{-\pi }{6}

 

Properties of Conjugate of Complex Number -

\bar{z_{1}}-\bar{z_{2}}=\overline{z_{1}-z_{2}}

- wherein

\bar{z} denotes conjugate of z

 

 


Option 1)

\frac{-\pi }{6}

This is correct

Option 2)

\frac{-\pi }{4}

This is incorrect

Option 3)

\frac{\pi }{4}

This is incorrect

Option 4)

\frac{\pi }{3}

This is incorrect

Posted by

prateek

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