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

Example 5 - Chapter 5 Class 11 Complex Numbers - Part 2

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Example, 5 Find the multiplicative inverse of 2 – 3i. Multiplicative inverse of z = z – 1 Multiplicative inverse of z = 1/𝑧 Putting z = 2 – 3i multiplicative inverse of 2 – 3i = 1/(2 βˆ’3𝑖) Rationalizing = 1/(( 2 βˆ’ 3𝑖 ) ) Γ—(( 2 + 3𝑖 ))/(( 2 + 3𝑖 ) ) = (2 + 3𝑖)/(( 2 βˆ’ 3𝑖 ) (2 + 3𝑖 ) ) Using ( a + b ) ( a – b ) = a2 – b2 = (2 + 3𝑖)/(2 2 βˆ’( 3𝑖 )2) = (2 + 3𝑖)/(4 βˆ’9𝑖^2 ) Putting i 2 = -1 = (2 + 3𝑖)/(4 βˆ’9 Γ—βˆ’1) = (2 + 3𝑖)/(4 + 9) = (2 + 3𝑖)/13 = 2/13 + 3𝑖/13 Hence, Multiplicative inverse = 2/13+3𝑖/13

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.