Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • If (1 + i)z = (1 – i) z ̅, then show that z= iz ̅

If (1 + i)z = (1 - i) \bar{z},  then show that z= -i\bar{z}

Answers (1)

(1 + i)z = (1 - i) \bar{z},

z=\frac{1-i}{1+i}\bar{z}

Rationalising the denominator,

\frac{\left (1-i \right )\left (1-i \right )}{\left (1+i \right )\left (1-i \right )}\bar{z}

=\frac{\left ( 1-i \right )^{2}}{1-i^2}\bar{z}

=\frac{\left ( 1-2i+i^2 \right )}{1+1}\bar{z}

=\frac{\left ( 1-2i-1 \right )}{2}\bar{z}

=-i\bar{z}

Hence,Proved.

 

Posted by

infoexpert21

View full answer

Similar Questions

Latest Question