Misc 9 - Chapter 4 Class 11 Complex Numbers

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Misc 9 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 14 years. He provides courses for Maths, Science and Computer Science at Teachoo