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  • Help me please, - Complex numbers and quadratic equations - JEE Main-2

z_{1} & z_{2}  are complex numbers such that \left |z_{1} \right |=1,\, \left |z_{2} \right |=2  and \left |z_{1}+z_{2} \right |=3 then  \left |\frac{1}{z_{1}}+\frac{4}{z_{2}} \right | equals 

  • Option 1)

    1

  • Option 2)

    2

  • Option 3)

    3

  • Option 4)

    4

 

Answers (1)

\left | Z_{1} \right |=1\Rightarrow Z_{1}\bar{Z_{1}}=1\Rightarrow \frac{1}{Z_{1}}=\bar{Z_{1}}        &              \left | Z_{2} \right |=2\Rightarrow Z_{2}\bar{Z_{2}}=4\Rightarrow \bar{Z_{2}}=\frac{4}{Z_{2}}

\left | \frac{1}{Z_{1}}+\frac{4}{Z_{2}} \right |=\left | \bar{Z_{1}}+\bar{Z_{2}} \right |=\left | \bar{Z_{1}+Z_{2}} \right |=\left | Z_{1}+Z_{2} \right |=3

 

Property of conjugate of complex number -

z\bar{z}=\left |z \right |^{2}

- wherein

  z=x+iy, \bar{z}=conjugate \: of\: z   

 \left |z \right |=\sqrt{x^{2}+y^{2}}

 

 


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

Vakul

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