Example 5 - Chapter 4 Class 11 Complex Numbers

Last updated at August 5, 2026 by

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

part 2 - Example 5 - Examples - Serial order wise - Chapter 4 Class 11 Complex Numbers

 

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Example, 5 Find the multiplicative inverse of 2 ā€“ 3i. Multiplicative inverse of z = z ā€“ 1 Multiplicative inverse of z = 1/š‘§ Putting z = 2 ā€“ 3i multiplicative inverse of 2 ā€“ 3i = 1/(2 āˆ’3š‘–) Rationalizing = 1/(( 2 āˆ’ 3š‘– ) ) Ɨ(( 2 + 3š‘– ))/(( 2 + 3š‘– ) ) = (2 + 3š‘–)/(( 2 āˆ’ 3š‘– ) (2 + 3š‘– ) ) Using ( a + b ) ( a ā€“ b ) = a2 ā€“ b2 = (2 + 3š‘–)/(2 2 āˆ’( 3š‘– )2) = (2 + 3š‘–)/(4 āˆ’9š‘–^2 ) Putting i 2 = -1 = (2 + 3š‘–)/(4 āˆ’9 Ɨāˆ’1) = (2 + 3š‘–)/(4 + 9) = (2 + 3š‘–)/13 = 2/13 + 3š‘–/13 Hence, Multiplicative inverse = 2/13+3š‘–/13

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