Last updated at March 9, 2017 by Teachoo

Transcript

Misc 4 If x โ iy = โ((a โ ib)/(c โ id)) prove that (๐ฅ2 + ๐ฆ2)^2 = (a^2 + b^2)/(c^2 + d^2 ) Introduction (๐ฅ โ ๐๐ฆ) (๐ฅ+ ๐๐ฆ) Using ( a โ b ) ( a + b ) = a2 โ b2 = (๐ฅ)^2 โ (๐๐ฆ)2 = ๐ฅ2 โ (๐) 2๐ฆ2 = ๐ฅ2 โ (โ 1)๐ฆ2 = ๐ฅ2 + ๐ฆ2 Misc 4 If x โ iy = โ((a โ ib)/(c โ id)) prove that (๐ฅ2 + ๐ฆ2)^2 = (a^2 + b^2)/(c^2 + d^2 ) Given ๐ฅ โ ๐๐ฆ = โ((a โ ib)/(c โ id)) Calculating ๐ฅ + ๐๐ฆ Replacing โ ๐ by ๐ ๐ฅ + ๐๐ฆ = โ((a + ib)/( c + id)) Multiplying (1) &(2) (๐ฅ โ๐๐ฆ) (๐ฅ+ ๐๐ฆ) = โ((a โ ib)/(c โ id)) ร โ((a + ib)/(c + id)) ๐ฅ2+๐ฆ2 =โ((aโib)/(cโid)ร(a + ib)/(c + id)) =โ((( a โ ib) (a + ib))/((c โ id) (c + id))) Using ( a โ b ) ( a + b ) = a2 โ b2 =โ(((a)^2 โ (ib)^2 )/((c)^2โใ (id)ใ^2 )) =โ((a^2 โ i^2 b^2 )/(c^2 โ i^2 d^2 )) Putting i2 = โ1 =โ((a2โ(โ1) b2 )/(c2โ(โ1)d2)) =โ((a2+ b2 )/(c + d2)) Hence, ๐ฅ2 + ๐ฆ2 =โ((a2+ b2 )/(c2 + d2)) Squaring both sides (x2 + y2)2 =(โ((a2+ b2 )/(c2 + d2)))^2 (x2 + y2)2 = (a2+ b2 )/(c2 + d2) Hence Proved

Miscellaneous

Misc 1
Important

Misc 2

Misc 3

Misc 4 Important You are here

Misc 5 (i) Deleted for CBSE Board 2022 Exams

Misc 5 (ii) Important

Misc 6

Misc 7

Misc 8 Important

Misc 9

Misc 10 Important

Misc 11

Misc 12

Misc 13 Important Deleted for CBSE Board 2022 Exams

Misc 14

Misc 15 Important

Misc 16

Misc 17 Important

Misc 18 Important

Misc 19

Misc 20 Important

Chapter 5 Class 11 Complex Numbers (Term 1)

Serial order wise

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.