Ex 5.1, 12 - Find multiplicative inverse of root 5 + 3i - Ex 5.1


  1. Chapter 5 Class 11 Complex Numbers
  2. Serial order wise
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Ex5.1, 12 Find the multiplicative inverse of the Complex number โˆš5 + 3๐‘– Multiplicative inverse of z = z โ€“ 1 Multiplicative inverse of z = 1/๐‘ง Putting z = โˆš5 + 3๐‘– multiplicative inverse of โˆš5 + 3๐‘– = 1/(โˆš5 + 3 ๐‘–) Rationalizing = 1/(โˆš5 + 3๐‘–) ร—(โˆš5 โˆ’ 3๐‘–)/(โˆš5 โˆ’ 3๐‘–) = (โˆš5 โˆ’ 3๐‘–)/(โˆš5 + 3๐‘– )(โˆš(5 )โˆ’ 3๐‘–) Using (a โ€“ b ) ( a + b ) = a 2 โ€“ b 2 = (โˆš5 โˆ’ 3๐‘–)/((โˆš5 )2โˆ’ (3๐‘–)2) "= " (โˆš5 โˆ’ 3๐‘–)/(5 โˆ’ 9๐‘–2) Putting i 2 = โˆ’1 = (โˆš5 โˆ’ 3๐‘–)/(5 โˆ’ 9 (โˆ’1) ) = (โˆš5 โˆ’ 3๐‘–)/(5 + 9 ) = (โˆš5 โˆ’ 3๐‘–)/14 = (โˆš5 )/14 โˆ’ 3/14 ๐‘–

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