

Examples
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 2022 Exams
Example 8 Important Deleted for CBSE Board 2022 Exams
Example 9
Example 10
Example 11 Important
Example 12
Example 13 (i) Important Deleted for CBSE Board 2022 Exams
Example 13 (ii) Deleted for CBSE Board 2022 Exams
Example 14 Important You are here
Example 15
Example 16 Important Deleted for CBSE Board 2022 Exams
Examples
Example 14 If x + iy = (a + ib)(𝑎 − 𝑖𝑏) Taking R.H.S a + ib𝑎 − 𝑖𝑏 Rationalizing = a + ib𝑎 − 𝑖𝑏 (a + ib)(𝑎+ 𝑖𝑏) = (a + ib)2 𝑎 − 𝑖𝑏 (𝑎 + 𝑖𝑏) = 𝑎2 + (𝑖𝑏)2 + 2𝑎𝑖𝑏 𝑎2 − (𝑖𝑏)2 = 𝑎2 + 𝑖2 𝑏2 + 2𝑎𝑖𝑏 𝑎2 − 𝑖2 ( 𝑏2) = 𝑎2 − 𝑏2 + 2𝑎𝑖𝑏 𝑎2 + 𝑏2 = 𝑎2 − 𝑏2 𝑎2 + 𝑏2 + i 2𝑎𝑏 𝑎2 + 𝑏2 Now L.H.S = x + iy Comparing real and imaginary parts in L.H.S and R.H.S Adding (1) and (2) 𝑥2+ 𝑦2= 𝑎2 − 𝑏2 𝑎2 + 𝑏22+ (2𝑎𝑏)2 ( 𝑎2 + 𝑏2)𝟐 = 1 ( 𝑎2 + 𝑏2)𝟐 𝑎2 − 𝑏22 + 2𝑎𝑏2 = 1 ( 𝑎2 + 𝑏2)𝟐 𝑎4 + 𝑏4−2 𝑎2 𝑏2+ 4𝑎2 𝑏2 = 𝑎2 2 + 𝑏22 + 2 𝑎2 𝑏2 ( 𝑎2 + 𝑏2)𝟐 = ( 𝑎2 + 𝑏2)𝟐 ( 𝑎2 + 𝑏2)𝟐 = 1 Thus, 𝑥2+ 𝑦2=1 Hence, Proved