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Last updated at Sept. 3, 2021 by Teachoo
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Example, 5 Find the multiplicative inverse of 2 โ 3i. Multiplicative inverse of z = z โ 1 Multiplicative inverse of z = 1/๐ง Putting z = 2 โ 3i multiplicative inverse of 2 โ 3i = 1/(2 โ3๐) Rationalizing = 1/(( 2 โ 3๐ ) ) ร(( 2 + 3๐ ))/(( 2 + 3๐ ) ) = (2 + 3๐)/(( 2 โ 3๐ ) (2 + 3๐ ) ) Using ( a + b ) ( a โ b ) = a2 โ b2 = (2 + 3๐)/(2 2 โ( 3๐ )2) = (2 + 3๐)/(4 โ9๐^2 ) Putting i 2 = -1 = (2 + 3๐)/(4 โ9 รโ1) = (2 + 3๐)/(4 + 9) = (2 + 3๐)/13 = 2/13 + 3๐/13 Hence, Multiplicative inverse = 2/13+3๐/13
Division
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