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  • Help me understand! - Complex numbers and quadratic equations - JEE Main-14

z is a complex number such that z+\bar{z}= 5 and z-\bar{z}= 7i then z equals 

  • Option 1)

    \frac{5}{2}-\frac{7}{2}i

  • Option 2)

    \frac{5}{2}+\frac{7}{2}i

  • Option 3)

    5+7i

  • Option 4)

    5-7i

 

Answers (1)

best_answer

z+\bar{z}=5

z-\bar{z}=7i

Adding both 2z=5+7i\: \Rightarrow \: z=\frac{5}{2}+\frac{7}{2}i

or

Re\left ( z \right )=\frac{z+\bar{z}}{2}=\frac{5}{2} \: and \: Im\left ( z \right )=\frac{z-\bar{z}}{2i}=\frac{7}{2}

\therefore Option (B)

 

Properties of Conjugate of a Complex Number -

Im(z)=\frac{z-\bar{z}}{2i}

- wherein

Im(z) denotes Imaginary part of z

\bar{z} denotes conjugate of z

 

 


Option 1)

\frac{5}{2}-\frac{7}{2}i

This is incorrect

Option 2)

\frac{5}{2}+\frac{7}{2}i

This is correct

Option 3)

5+7i

This is incorrect

Option 4)

5-7i

This is incorrect

Posted by

prateek

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