Examples

Example 1

Example 2 (i)

Example 2 (ii) Important

Example 3

Example 4

Example 5 Important

Example 6 (i)

Example 6 (ii) Important

Example 7 Deleted for CBSE Board 2023 Exams

Example 8 Important Deleted for CBSE Board 2023 Exams

Example 9 Deleted for CBSE Board 2023 Exams

Example 10 Deleted for CBSE Board 2023 Exams

Example 11 Important Deleted for CBSE Board 2023 Exams

Example 12 You are here

Example 13 (i) Important

Example 13 (ii)

Example 14 Important

Example 15

Example 16 Important Deleted for CBSE Board 2023 Exams

Last updated at Dec. 8, 2016 by Teachoo

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