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Misc 9 - Chapter 4 Class 11 Complex Numbers
Last updated at April 16, 2024 by Teachoo
Chapter 4 Class 11 Complex Numbers
Concept wise
- Quadaratic equation
- Two complex numbers equal
- Convert to a + ib form
- Identities (square, cube of 2 complex numbers)
- Division
- Power of i(odd and even)
- Conjugate
-
Modulus,argument
- Polar representation
- Proof- Replacing iota with -iota
- Proof- Taking general complex numbers
- Proof- Solving
- Proof- Using modulus conjugate property (Pg 102)
Transcript
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
