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Ex 5.1, 11 - Find multiplicative inverse of 4 - 3i - Ex 5.1

  1. Chapter 5 Class 11 Complex Numbers
  2. Serial order wise
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Ex5.1, 11 Find the multiplicative inverse of the Complex number 4 โ€“ 3๐‘– Multiplicative inverse of z = z โ€“ 1 Multiplicative inverse of z = 1/๐‘ง Putting z = 4 โ€“ 3i multiplicative inverse of 4 โ€“ 3i = 1/(4 โˆ’3 ๐‘–) Rationalizing = 1/(4 โˆ’3๐‘–) ร—(4 + 3๐‘–)/(4 + 3๐‘–) = (4+3i)/(4 โˆ’3i)(4 + 3๐‘–) Using (a โ€“ b ) ( a + b ) = a 2 โ€“ b 2 = (4 + 3๐‘–)/((4)2โˆ’(3๐‘–)2) = (4 + 3i)/(16 โˆ’ 9๐‘–2) Putting i 2 = โˆ’ 1 = (4 + 3๐‘–)/(16 โˆ’9 (โˆ’1) ) = (4 + 3๐‘–)/(16 + 9) = (4 + 3๐‘–)/25 = 4/25+3/25 ๐‘–

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