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  • Try this! - Complex numbers and quadratic equations - JEE Main-4

z_{1} & z_{2} are complex numbers such that arg\left (z_{1} \right )= arg\left (z_{2} \right ) then

  • Option 1)

    z_{1}\bar{z_{2}}+\bar{z_{1}}z_{2}= 0

  • Option 2)

    z_{1}z_{2}+\bar{z_{1}}\bar{z_{2}}= 0

  • Option 3)

    z_{1}\bar{z_{2}}-\bar{z_{1}}z_{2}= 0

  • Option 4)

    z_{1}z_{2}-\bar{z_{1}}\bar{z_{2}}= 0

 

Answers (1)

best_answer

arg(z_{1})= arg(z_{2})

arg(z_{1})- arg(z_{2})=0

arg(z_{1}) /(z_{2})=0

(z_{1}) /(z_{2}) is real 

so (z_{1}) /(z_{2})= \overline{(z_{1}) /(z_{2})}

z_{1}\bar{z_{2}}-\bar{z_{1}}z_{2} =0

 

Properties of Argument of a Complex Number -

Arg(z)=0\Rightarrow z\ is\ real\Rightarrow z=\bar{z}

- wherein

Arg(z) denotes Argument of z and \bar{z} denotes conjugate of z

 

 

 


Option 1)

z_{1}\bar{z_{2}}+\bar{z_{1}}z_{2}= 0

This is incorrect

Option 2)

z_{1}z_{2}+\bar{z_{1}}\bar{z_{2}}= 0

This is incorrect

Option 3)

z_{1}\bar{z_{2}}-\bar{z_{1}}z_{2}= 0

This is correct

Option 4)

z_{1}z_{2}-\bar{z_{1}}\bar{z_{2}}= 0

This is incorrect

Posted by

divya.saini

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