Ex 5.1, 12 - Chapter 5 Class 11 Complex Numbers (Term 1)
Last updated at Sept. 3, 2021 by Teachoo
Ex 5.1
Last updated at Sept. 3, 2021 by Teachoo
Ex5.1, 12 Find the multiplicative inverse of the Complex number √5 + 3𝑖 Multiplicative inverse of z = z – 1 Multiplicative inverse of z = 1/𝑧 Putting z = √5 + 3𝑖 multiplicative inverse of √5 + 3𝑖 = 1/(√5 + 3 𝑖) Rationalizing = 1/(√5 + 3𝑖) ×(√5 − 3𝑖)/(√5 − 3𝑖) = (√5 − 3𝑖)/(√5 + 3𝑖 )(√(5 )− 3𝑖) Using (a – b ) ( a + b ) = a 2 – b 2 = (√5 − 3𝑖)/((√5 )2− (3𝑖)2) "= " (√5 − 3𝑖)/(5 − 9𝑖2) Putting i 2 = −1 = (√5 − 3𝑖)/(5 − 9 (−1) ) = (√5 − 3𝑖)/(5 + 9 ) = (√5 − 3𝑖)/14 = (√5 )/14 − 3/14 𝑖