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z_{1} & z_{2} are two complex numbers such that  \frac{z_{1}}{z_{1}}= \frac{-z_{2}}{z_{2}}  ,  \left |z_{1} \right |= 5 and \left |z_{2} \right |=12, then \left |z_{1}+z_{2} \right | equals

  • Option 1)

    12

  • Option 2)

    13

  • Option 3)

    14

  • Option 4)

    15

 

Answers (1)

best_answer

\frac{z_{1}}{\bar{z_{1}}}=\frac{-z_{2}}{\bar{z_{2}}}\: \Rightarrow \: z_{1}\bar{z_{2}}+\bar{z_{1}}z_{2}=0

We know, \left | z_{1}+z_{2} \right |^{2}=\left | z_{1} \right |^{2}+\left | z_{2} \right |^{2}+\left ( z_{1}\bar{z_{2}}+\bar{z_{1}}z_{2} \right )

\therefore \left | z_{1}+z_{2} \right |^{2}=25+144+0

\therefore \left | z_{1}+z_{2} \right |=13

\therefore Option (B)

 

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)

12

This is incorrect

Option 2)

13

This is correct

Option 3)

14

This is incorrect

Option 4)

15

This is incorrect

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prateek

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