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Misc 15 - Chapter 5 Class 11 Complex Numbers (Term 1)

Last updated at March 22, 2023 by

Misc 15 - Find modulus of (1 + i)/(1 - i) - (1 - i)/(1 + i) - Modulus,argument

Misc 15 - Chapter 5 Class 11 Complex Numbers - Part 2
Misc 15 - Chapter 5 Class 11 Complex Numbers - Part 3

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Misc 15 Find the modulus of (1 + )/(1 ) (1 )/(1 + ) First we solve (1 + )/(1 ) (1 )/(1 + ) (1 + )/(1 ) (1 )/(1 + ) = ((1 + ) (1 + ) (1 ) (1 ))/((1 ) (1+ )) = ((1 + )2 ( 1 )2)/((1 ) (1 + )) Using a2 b2 = (a + b) (a b) = ([( 1+ ) + ( 1 )] [( 1+ ) ( 1 )])/((1)2 ( )2) = (( 1 + 1 + ) ( + + 1 1 ))/( 1 2) = (( 2 + 0 ) ( 2 + 0 ))/(1 2) = ((2) (2 ))/(1 2) = 4 /(1 2) Putting i2 = - 1 = 4 /( 1 ( 1 ) ) = 4 /( 1 + 1) = ( 4 )/( 2) = 2 = 0 + 2 Thus , (1 + )/(1 ) (1 )/(1 + ) = 0 + 2 Thus , (1 + )/(1 ) (1 )/(1 + ) = 0 + 2 We need to find modulus of (1 + )/(1 ) (1 )/(1 + ) Complex number (0 + 2 ) is of the form x + y Hence x = 0 and y = 2 Modulus of z = |z| |z| = ( ^2+ 2) = ((0)2+(2)2) = (0+4) = 4 = 2 Hence, Modulus of (1 + )/(1 ) (1 )/(1 + ) = 2

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.