Example 5 - Find multiplicative inverse of 2 - 3i - CBSE - Division

  1. Chapter 5 Class 11 Complex Numbers
  2. Serial order wise

Transcript

Example, 5 Find the multiplicative inverse of 2 โ€“ 3i. Multiplicative inverse of z = z โ€“ 1 Multiplicative inverse of z = 1/๐‘ง Putting z = 2 โ€“ 3i multiplicative inverse of 2 โ€“ 3i = 1/(2 โˆ’3๐‘–) Rationalizing = 1/(( 2 โˆ’ 3๐‘– ) ) ร—(( 2 + 3๐‘– ))/(( 2 + 3๐‘– ) ) = (2 + 3๐‘–)/(( 2 โˆ’ 3๐‘– ) (2 + 3๐‘– ) ) Using ( a + b ) ( a โ€“ b ) = a2 โ€“ b2 = (2 + 3๐‘–)/(2 2 โˆ’( 3๐‘– )2) = (2 + 3๐‘–)/(4 โˆ’9๐‘–^2 ) Putting i 2 = -1 = (2 + 3๐‘–)/(4 โˆ’9 ร—โˆ’1) = (2 + 3๐‘–)/(4 + 9) = (2 + 3๐‘–)/13 = 2/13 + 3๐‘–/13 Hence, Multiplicative inverse = 2/13+3๐‘–/13

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