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

  • Option 1)

    13

  • Option 2)

    \frac{1}{13}

  • Option 3)

    325

  • Option 4)

    \frac{1}{325}

 

Answers (1)

\left | \frac{z_{1}}{z_{2}} \right |=\frac{\left |z_{1} \right |}{\left |z_{2} \right |}=5\cdots \cdots \left ( 1 \right )

\left | \frac{z_{2}}{z_{3}} \right |=\frac{\left |z_{2} \right |}{\left |z_{3} \right |}=13\cdots \cdots \left (2 \right )

\frac{\left |z_{1} \right |}{\left |z_{3} \right |}=65

Since \left |z_{1} \right |=5\Rightarrow \left |z_{3} \right |=\frac{5}{65}=\frac{1}{13}

\therefore Option (B)

 

Property of Modulus of z(Complex Number) -

\left |\frac{z_{1}}{z_{2}} \right |=\frac{\left |z_{1} \right |}{\left |z_{2} \right |}

- wherein

|.| denotes modulus of complex number

 

 


Option 1)

13

This is incorrect

Option 2)

\frac{1}{13}

This is correct

Option 3)

325

This is incorrect

Option 4)

\frac{1}{325}

This is incorrect

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