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  • I need help with - Complex numbers and quadratic equations - JEE Main-3

z_{1}=-3+2i & z_{2}=a-i are equidistant from z_{3}=1-5i then a equals 

  • Option 1)

    5,-6

  • Option 2)

    6,8

  • Option 3)

    8,-6

  • Option 4)

    -8,6

 

Answers (1)

best_answer

Distance between   Z_{1} and Z_{2}=\left | Z_{1}-Z_{3} \right |=\left | -4+ji \right |=\sqrt{65}

Distance between  Z_{2} and Z_{3}=\left | Z_{2}-Z_{3} \right |=\left | \left ( a-1 \right )+4i \right |=\sqrt{\left ( a-1 \right )^{2}+16}

\Rightarrow \sqrt{65}=\sqrt{\left ( a-1 \right )^{2}+16}\Rightarrow \left ( a-1 \right )^{2}=49\Rightarrow a=8,-6

 

Distance between Z1 and Z2 -

\left | z_{1}-z_{2} \right |=\left | \left (x_{1}-x_{2} \right )+i\left ( y_{1}-y_{2} \right ) \right |=\sqrt{\left (x_{1}-x_{2} \right )^{2}+\left ( y_{1}-y_{2} \right )^{2}}=  Distance between points \left (x_{1},y_{1} \right ) & \left (x_{2},y_{2} \right ) = distance between z_{1} and z_{2} 

- wherein

z_{1} & z_{2} are any two complex numbers , z_{1}=x_{1}+iy_{1} , z_{2}=x_{2}+iy_{2}

 

 


Option 1)

5,-6

This is incorrect

Option 2)

6,8

This is incorrect

Option 3)

8,-6

This is correct

Option 4)

-8,6

This is incorrect

Posted by

Aadil

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