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Examples
Last updated at Sept. 3, 2021 by Teachoo
Example, 5 Find the multiplicative inverse of 2 β 3i. Multiplicative inverse of z = z β 1 Multiplicative inverse of z = 1/π§ Putting z = 2 β 3i multiplicative inverse of 2 β 3i = 1/(2 β3π) Rationalizing = 1/(( 2 β 3π ) ) Γ(( 2 + 3π ))/(( 2 + 3π ) ) = (2 + 3π)/(( 2 β 3π ) (2 + 3π ) ) Using ( a + b ) ( a β b ) = a2 β b2 = (2 + 3π)/(2 2 β( 3π )2) = (2 + 3π)/(4 β9π^2 ) Putting i 2 = -1 = (2 + 3π)/(4 β9 Γβ1) = (2 + 3π)/(4 + 9) = (2 + 3π)/13 = 2/13 + 3π/13 Hence, Multiplicative inverse = 2/13+3π/13