Misc 11 - Chapter 4 Class 11 Complex Numbers
Last updated at April 16, 2024 by Teachoo
Miscellaneous
Misc 1
Important
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Chapter 4 Class 11 Complex Numbers
Serial order wise
Transcript
Misc 11 If and are different complex numbers with | | = 1, then find |( " " )/(1 )| . We know that |z|2 = (z) ( ) |( )/(1 )|^2=(( )/(1 )) ((( )/(1 )) ) = (( )/(1 )) (( ) /(1 ) ) = (( )/(1 )) (( )/(1 )) = (( )/(1 )) (( )/(1 )) = (( )( ))/((1 )(1 )) = ( ( ) ( ))/(1 (1 ) (1 ) ) = ( + )/(1 + ) = (| |^2 + | |^2)/(1 +| |^2 | |^2 ) Given that | |=1 So, | |^2=1 = (1 + | |^2)/(1 + | |^2 1) = (1 + | |^2)/(1 + | |^2 ) = 1 Hence |( )/(1 )|^2 = 1 |( )/(1 )| = 1 |( )/(1 )| =1
