Ex 4.1, 12 - Chapter 4 Class 11 Complex Numbers

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Ex 4.1, 12 - Find multiplicative inverse of root 5 + 3i - Ex 4.1 - Ex 4.1

part 2 - Ex 4.1, 12 - Ex 4.1 - Serial order wise - Chapter 4 Class 11 Complex Numbers


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Ex5.1, 12 Find the multiplicative inverse of the Complex number āˆš5 + 3š‘– Multiplicative inverse of z = z ā€“ 1 Multiplicative inverse of z = 1/š‘§ Putting z = āˆš5 + 3š‘– multiplicative inverse of āˆš5 + 3š‘– = 1/(āˆš5 + 3 š‘–) Rationalizing = 1/(āˆš5 + 3š‘–) Ɨ(āˆš5 āˆ’ 3š‘–)/(āˆš5 āˆ’ 3š‘–) = (āˆš5 āˆ’ 3š‘–)/(āˆš5 + 3š‘– )(āˆš(5 )āˆ’ 3š‘–) Using (a ā€“ b ) ( a + b ) = a 2 ā€“ b 2 = (āˆš5 āˆ’ 3š‘–)/((āˆš5 )2āˆ’ (3š‘–)2) "= " (āˆš5 āˆ’ 3š‘–)/(5 āˆ’ 9š‘–2) Putting i 2 = āˆ’1 = (āˆš5 āˆ’ 3š‘–)/(5 āˆ’ 9 (āˆ’1) ) = (āˆš5 āˆ’ 3š‘–)/(5 + 9 ) = (āˆš5 āˆ’ 3š‘–)/14 = (āˆš5 )/14 āˆ’ 3/14 š‘–

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