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Misc 17 - Chapter 5 Class 11 If are different complex numbers - Proof- Using modulus conjugate property (Pg 102)

Misc 17 - Chapter 5 Class 11 Complex Numbers - Part 2
Misc 17 - Chapter 5 Class 11 Complex Numbers - Part 3

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Misc 17 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

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.