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  • Help me please, - Complex numbers and quadratic equations - JEE Main-12

Let z_{1}= 3-4i and z_{1}z_{2}= 12-5i, then \left | z_{2} \right |  equals

  • Option 1)

    \frac{5}{13}

  • Option 2)

    \frac{13}{5}

  • Option 3)

    \frac{5}{12}

  • Option 4)

    \frac{12}{5}

 

Answers (1)

best_answer

we know, \left | z_{1}z_{2} \right |=\left | z_{1} \right |\left | z_{2} \right |\Rightarrow \left | z_{2} \right |=\frac{\left | z_{1}z_{2} \right |}{z_{1}}

Here, \left | z_{1}z_{2} \right |=\sqrt{144+25}=13\: and\: \left | z_{1} \right |=\sqrt{9+16}=5

\therefore \left | z_{2} \right |=\frac{13}{5}

\therefore Option (B)

 

Property of Modulus of z(Complex Number) -

|z1z2|=|z1||z2|

- wherein

|.| denotes modulus of complex number

 

 


Option 1)

\frac{5}{13}

This is incorrect

Option 2)

\frac{13}{5}

This is correct

Option 3)

\frac{5}{12}

This is incorrect

Option 4)

\frac{12}{5}

This is incorrect

Posted by

Aadil

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