Ex5.1, 11
Find the multiplicative inverse of the Complex number 4 – 3𝑖
Multiplicative inverse of z = z – 1
Multiplicative inverse of z = 1/𝑧
Putting z = 4 – 3i
multiplicative inverse of 4 – 3i = 1/(4 −3 𝑖)
Rationalizing
= 1/(4 −3𝑖) ×(4 + 3𝑖)/(4 + 3𝑖)
= (4+3i)/(4 −3i)(4 + 3𝑖)
Using (a – b ) ( a + b ) = a 2 – b 2
= (4 + 3𝑖)/((4)2−(3𝑖)2)
= (4 + 3i)/(16 − 9𝑖2)
Putting i 2 = − 1
= (4 + 3𝑖)/(16 −9 (−1) )
= (4 + 3𝑖)/(16 + 9)
= (4 + 3𝑖)/25
= 4/25+3/25 𝑖

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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