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The conjugate of a complex number is \frac{1}{i-1}. Then that complex number is

  • Option 1)

    \frac{1}{i-1}

  • Option 2)

    \frac{-1}{i-1}

  • Option 3)

    \frac{1}{i+1}

  • Option 4)

    \frac{-1}{i+1}

 

Answers (3)

best_answer

As we learnt in

Properties of Conjugate of Complex Number -

\bar{z_{1}}+\bar{z_{2}}=\overline{z_{1}+z_{2}}

- wherein

\bar{z} denotes conjugate of z

 

 \frac{1}{i-1}=\frac{i+1}{-2}=z

\therefore\ \; \bar{z}=\frac{1-i}{-z}

\therefore\ \; \frac{(1-i)(1+i)}{-2(1+i)}=\frac{2}{-2(i+1)}=\frac{-1}{1+i}

Put -i at the place on i=\frac{-1}{1+i}.

Correct option is 4.

 


Option 1)

\frac{1}{i-1}

This is an incorrect option.

Option 2)

\frac{-1}{i-1}

This is an incorrect option.

Option 3)

\frac{1}{i+1}

This is an incorrect option.

Option 4)

\frac{-1}{i+1}

This the correct option.

Posted by

prateek

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1/I+1

Posted by

J vamshi

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