Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class

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

Example 8 Important You are here

Question 1 Deleted for CBSE Board 2024 Exams

Question 2 Important Deleted for CBSE Board 2024 Exams

Question 3 Deleted for CBSE Board 2024 Exams

Question 4 Deleted for CBSE Board 2024 Exams

Question 5 Important Deleted for CBSE Board 2024 Exams

Question 6 (i) Important Deleted for CBSE Board 2024 Exams

Question 6 (ii) Deleted for CBSE Board 2024 Exams

Question 7 Deleted for CBSE Board 2024 Exams

Question 8 Important Deleted for CBSE Board 2024 Exams

Last updated at May 29, 2023 by Teachoo

Example 8 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