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  • Please,please help me - Complex numbers and quadratic equations - JEE Main-7

z_{1} and z_{2} are two complex numbers such that \left | z_{1}+z_{2} \right |= 4,\: \left | z_{1} \right |= 3  and  \left | z_{2} \right |= 2 then z_{1}\bar{z_{2}}+\bar{z_{1}}z_{2}  equal

  • Option 1)

    1

  • Option 2)

    2

  • Option 3)

    3

  • Option 4)

    4

 

Answers (1)

best_answer

\because \left | z_{1}+z_{2} \right |^{2}=\left | z_{1} \right |^{2}+\left | z_{2} \right |^{2}+z_{1}\bar{z_{2}}+\bar{z_{1}}z_{2}

\Rightarrow \: z_{1}\bar{z_{2}}+\bar{z_{1}}z_{2}=16-9-4=3

\therefore Option (C)

 

Property of Modulus of z(Complex Number) -

|z_{1}+z_{2}|^{2}=\left | z_{1} \right |^{2}+\left | z_{2} \right |^{2}+z_{1}.\bar{z_{2}}+z_{2}.\bar{z_{1}}

- wherein

|.| denotes modulus of z

\bar{z} denotes conjugate of z

 

 


Option 1)

1

This is incorrect

Option 2)

2

This is incorrect

Option 3)

3

This is correct

Option 4)

4

This is incorrect

Posted by

divya.saini

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