Check sibling questions

Example 12 - Find conjugate of (3 - 2i)(2 + 3i)/(1 + 2i) - Conjugate

Example 12 - Chapter 5 Class 11 Complex Numbers - Part 2
Example 12 - Chapter 5 Class 11 Complex Numbers - Part 3 Example 12 - Chapter 5 Class 11 Complex Numbers - Part 4


Transcript

Example 12 Find the conjugate of ((3 − 2i)(2 + 3i))/((1 + 2i)(2 − i) ) First we calculate ((3 − 2i)(2 + 3i))/((1 + 2i)(2 − i) ) then find its conjugate ((3 −2i)(2+3i))/((1+ 2i)(2−i) ) = (3(2+3i)−2i(2+3i))/(1(2−i)+ 2i(2−i) ) = (3 × 2 +3 × 3𝑖 − 2𝑖 × 2 − 2𝑖 × 3𝑖)/(1 × 2 + 1 ×( −𝑖) + 2𝑖 × 2 − 2𝑖 × 𝑖 ) = (6 + 9i − 4i + 6𝑖2)/(2 − i + 4i − 2i2) = (6 + 5i − 6𝑖2)/(2 + 3i + 2i2) Putting i2 = −1 = (6 + 5𝑖 − 6 ( −1))/(2 + 3𝑖 −2( −1)) = (6 + 5𝑖 + 6)/(2 + 3𝑖 + 2) = (6 + 6 + 5𝑖)/(2 + 2 + 3𝑖) = (12 + 5𝑖)/(4 + 3𝑖) Rationalizing = (12 + 5𝑖)/(4 + 3𝑖) × (4 − 3𝑖)/(4 − 3𝑖) = ((12 + 5𝑖) (4 − 3𝑖))/((4 + 3𝑖) (4 − 3𝑖) ) = (12 × 4 − 12 × 3𝑖 + 5𝑖 × 4 − 5𝑖 × 3𝑖)/((4 + 3𝑖) (4 − 3𝑖)) = (48 − 36𝑖 + 20𝑖 −15𝑖2)/((4 + 3𝑖) (4 − 3𝑖)) Putting i2 = − 1 = (48 − 16𝑖 − 15 (−1))/((4 + 3𝑖) (4 − 3𝑖)) = (48 − 16𝑖 +15)/((4 + 3𝑖) (4 − 3𝑖)) = (63 − 16𝑖)/((4 + 3𝑖) (4 − 3𝑖)) Using (a – b) (a + b) = a2 – b2 = (63 − 16𝑖)/((4)2 − (3𝑖)2 ) = (63 − 16𝑖)/(16 −9𝑖2) Putting i2 = − 1 = (63 −16𝑖)/(16 + 9(−1) ) = (63 − 16𝑖)/(16 + 9) = (63 − 16𝑖)/25 Hence, ((3 −2i)(2+3i))/((1+ 2i)(2−i) ) = 63/25 − 16/25 𝑖 So conjugate of ((3 −2i)(2+3i))/((1+ 2i)(2−i) ) is 63/25 + 16/25 𝑖

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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 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.